Hey there! My cat had almost the same exact problems as your's with the exception of giardia. I went through a seven month ordeal treating him because his ringworm was so severe. We finally got it cleared up but I can give you some advice.
Rupert lived in me in my room when I first got him (we were introducing him to the dog but were worried how that would pan out so he just hung out with me). He never showed any signs, but I began to be covered in spots. At first I thought it was flees, but eventually they spread and basically, I was covered everywhere. Vet did the culture and bam - ringworm.
He was started on oral medications when he was 4 months old. His first one was Griseofulvin. Because I was so severely susceptible to developing ringworm (seriously, it was on my face, all over my legs, I was excruciatingly depressed because of it), we confined Ru to my bathroom. Make sure you take away EVERYTHING when you do this - even the sink handles if you can (he eventually learned how to turn the sink on himself when we weren't home...cue flooding).
We were to bleach the bathroom twice a week while confining Rupert to a crate that could later also be easily bleached out (had this down to a science towards the end. Fill a bucket with the bleach solution & water, fill a spray bottle, use the bucket to mop out the floor and wash down the shower, use the bottle to spray down everything else (walls, cabinets, mirror, etc. Luckily our bathroom is white). He cried, it was hard. I had special bathroom-only clothes (long sleeves) that I wore with gloves so I could play with him and still socialize him. I was so heartbroken over it, and trust me, I felt guilty.
He cried a lot. I left the window blinds open because I wanted him to have some kitty-tv during the day. My neighbors called animal control because they thought we were abusing him. Imagine having to explain to an officer your situation that you're already super worked up about; it sucked. Shortly after that, we had him neutered and the crying slowly died down. He still said hello everytime someone came home or walked past the door, but he did mellow out a lot.
AFTER that, he had an allergic reaction to the griseofulvin. We switched him over to a fluconazole + itraconazole mix. Around this time, I started looking into lime sulfur dips, but our vet said he had little success with them + they smelled terrible. Bleach was already burning my nasal cavities out but we decided to give the new orals a try.
Rupert decided he didn't like the taste of these meds and began spitting them out or eating around them when we hid them in medication snack pockets. So we started to crush them up and hide them in baby foods (if you go this route, make sure they're onion powder free) for him.
We were going for woods lamp checks and cultures about every 4 weeks. There was very little progress being made and he was starting to show signs of scabbing/actual ringworm (instead of being super asymptomatic as he was).
FINALLY, our vet consulted with a specialized dermatologist that only visits the office about once a year. After that, we were prescribed a ketoconazole shampoo with a chlorhexidine leave in conditioner to use twice weekly for 4 weeks. (I believe the brands for the shampoo was Ketochlor, I think the conditioner was something generic but I can check those for you if you want). He improved DRAMATICALLY. At the end of 4 weeks, he had ONE spot show up during the woods lamp check - when previously he pretty much lit up like a Christmas tree. And trust me, after 5 months of this ordeal, it was like the best present I could ask for.
We continued the baths once a week for eight more weeks and Rupert was finally determined ringworm free after that. Even then, I still continued the baths every other week for two months (he's part himalayan anyways so his long fur usually gets dirty).
Nobody should go through what I went through. But our vet was set on not putting Ru through lime sulphur dips (I vaguely remember something being mentioned about eye irritant as well and how because Rupert does have herpes & eye mucus buildup, he didn't want to have to put him through that ordeal).
There are somethings I did learn from this ordeal though, and I hope you don't mind my very long story! I found it easier to find people that had actually made it through the ringworm process rather than those that pretty much spelled it out as a death sentence for you & all of your belongings.
What I did do: For the bathroom kitty, line the litter box with a garbage bag (or two if your kitty likes to scratch through it). This way it's easy to clean when it comes time to bleach the bathroom. Also get plastic toys - I know the string toys are tempting (I pretty much bought a new one for Ru each week), but the plastic ones you can just leave to bleach in the bucket while you wash down the rest of the bathroom. Also, they have disposable scratching posts! So I would get those when I had the chance as well :) The little cardboard ones that come in refill kits work pretty well. Finally, I forgot to mention this before but WASH DOWN the bathroom after the bleach has dried. Usually, I would bleach everything, set a timer for 10 minutes, refill my bucket & spray bottle with tap water, turn the shower on and go back in to give everything a nice rinse-over then let that dry for 10 more minutes. It's not super necessary, but I was very concerned that Rupert would find a puddle somewhere I had left and start licking it up. Lastly, get some designated bleach towels so you can wipe down those parts that just would not dry when it came time to put kitty back in his room. Also pro-tip- if your cat is a longhair like mine, or if he generally finds away to make a mess, OR if you have an open radiator/heater in your bathroom, it's a good idea to get a vacuum to clean the bathroom out with before you wash it down (and it does make you feel like you're killing all these stupid ringworm spores). I know it sounds like a lot but after a week or two of doing it, you get the hang of it. And don't fall for any of those stupid forums that say you need -THE BEST- vacuums with prime filters or whatever. Just get a regular old vacuum that you can take apart and spray the inside down with bleach when you're done.
Also, I didn't throw everything away like everybody suggested. I got some anti-bacterial liquid detergent (I know ringworm is a fungus but I couldn't find anything for colors that had safe-bleach in it at Costco) and I just used that + washed EVERYTHING in warm water only for seven months straight. Seemed to work fine for me.
I did spray the hardwood floors of my room over with bleach, they came out fine but unfortunately my walls do need a paint job still from the droplets.
Finally, a suggestion for any cosmetic products - get rid of them. Especially if you used them on a spot that you didn't realize had ringworm. I spread so much ringworm because of my concealer and I had no idea (which is how I ended up with it all over my face). Also, PLEASE don't scratch the spots. Basically consider it to be poison ivy. If you touch one spot then somewhere else on your body, it will show up. And if it does get out of hand, convince your dermatologist you do need the big, liver-killer medications. Don't let her try to tell you that the cream or whatever she prescribed is going to make it go away in a /few weeks/.
And I guess some other kitty tips? My cat was so lonely that towards the end, we started wrapping him in his own designated towels and then let him come sit with us in other rooms of the house. He was so happy to have some time with us that he was content sitting in our laps like that for hours. If anything, his time in the bathroom has made him now a super affectionate lap kitty. Just spend time with your new household member and don't let the internet scare you :) Ringworm does suck a ton, but there's a light at the end of the tunnel.