OP, I was just like you up until about 7 months ago. I'm 26, just got a non-contract full time job since college.
I recently started feeling comfortable with money as I was a contractor for a few years after college. When one ended 4 months after I started (and was supposed to be a year), I always felt like it would happen again. I would have analysis paralysis about necessary purchases (like new pants for work) walk in the store after reseraching, try them on, walk out, sit on the decision for weeks, not buy them, and then go through the whole thing again. My boyfriend had to get me out of that. Now that I can save with a steady job, I'm stressing less. I still have moments where I think I don't have enough, but I do. You can't starve or go naked. I just buy quality on sale, try to plan as best as possible with wiggle room.
A budget is there to keep you on track, and to adjust as needed. It shouldn't be to paralyze you. What really helped me was that I set a savings goal, and try to adjust every 6 months if I can. I set my savings goal 10% for myself when I was a contractor making $35 pre-tax, rent was 50% of my income (2nd contract paid 30% less than 1st and I had a surgery that I had gobs of bills). It's literally all I could manage since I had medical bills. Now that I'm full time 7 months, I bumped it to 20% for 6 months which was a comfortable spot. I just bumped it to 30%, which is probably where I'll stay for a bit because it's a challenge and I feel that 10%, but I know if I need it, I can use it. I do auto direct deposit so I don't have to worry about saving, it's done for me. What goes in checking is mine for bills, anything else, but at the end of the month, I just dump what's left for extra savings. Or buy myself that 1 new bottle of nail polish I saw at Target and put the rest away :) It's about controlled spending, not about it controlling you!
My car is 16 years old with 210k miles, so I know I'll need one soon, but if she breaks tomorrow and I don't have $15k to buy one out right, there's nothing I can do in that instance. I'll use some savings to put down a down payment and keep moving.
I started using a manual transaction app called Expense IQ in college that I could set a budget for and bills at the beginning of the month, and as I'd spend money, I would take 10 seconds to put in the transaction and it would update whatever category it's assigned to (i.e. spend $10 at the grocery store, budget was set at $150, I now have $140 left). It helped put my mind at ease, unless you can't remember to put in transactions.
Now that I feel more comfortable with money, I just check in every few days with an app called Level Money. I like it way better than Mint as it's a bit simpler, but essentially it's not to track your saving, just spending. It assumes you're already saving something, and then it pulls spending from credit cards, debit accounts into one area. You set a spendable amount (after bills are put in) for the month, which can be adjusted.The app tells you how much you've spent over the course of months to help you adjust that amount, and you can categorize transactions. At one glance, you can see how much you've spent in each category for the month, as well as how much you have left for the month. Apparently it's geard towards college kids, but I really like it and it's free.
Sorry for the long post, but I get where you're coming from. You have to live a little :)