Agreed, hair conditioner is the best thing for shaving. I use cheap Costco brand stuff and it works great. Decent for actually taking care of my hair too. Against the grain works well if you're looking for a very close shave, as a trans woman achieving is a vital survival skill, but going with the grain is a lot less apt to leave you with cuts and irritation. In your case it might be worth taking the gentler route, especially if you don't mind doing it more frequently. If it's only a couple of areas, adding shaving to your shower routine should be pretty easy.

That nothing can be done for PCOS is absolutely false and you need to see a better doctor, whether or not they're right about insurance not covering a test. Spironolactone is an effective, reasonably cheap anti-androgen (as in it reduces testosterone levels) that almost any insurance should cover. It's also a diuretic but other than that the side effects aren't generally bad. Not a permanent treatment but if you have a hormonal imbalance, it should make you feel better, and it's safe enough to be prescribed long term. There are tons of girls who have been taking it for years. Unfortunately I can't tell you much beyond that, it's not my area of expertise. Don't give up on getting diagnosed and treated though.

If you ever want to look into permanent hair removal, laser is pretty cheap (I paid $100 a session for full face thought that's on the low end). How effective it is depends on a variety of factors, particularly how much darker your hair is than your skin, and there's an element of luck in there as well. It's not going to complete removal but it can help. Electrolysis is much more efficient at killing hair follicles but it's also a lot more expensive. Still might be worth checking out someday, it would save time and shaving supplies in the long run. You can generally get a free consultation to find out how much the hair removal you're looking for would cost. But that's all up to you, just putting information out there.

As far as razors, Dorco are dirt cheap and reasonably decent. If you've heard of Dollar Shave Club, they're just selling Dorco razors and you can buy them directly for less. The plastic that connects the blade to the handle on the ones I'm using seems to break after about a month but at that point the blade is pretty dull anyway. Gillette is the gold standard and they really are better quality but you're going to pay a lot more, I don't think it's worth the trade off personally but I'm also very low income.

Hope some of that helps!