I feel you, I also get stressed out during interviews and perform worse than normally; it was the same for me during oral exams at Uni.

At one point I interviewed at a couple big ones and got into FB, where I also did a fair amount of interviewing. My tips:

1. Accept it's a numbers game; apply to N, and you'll get an offer from one. I got rejected by Google and Spotify, got an offer from FB. Some people do better and get more offers, but I know I'm a nervous type during interviews and under-perform. It's okay, it's a First World Problem, just apply to more companies. I think most people I know who work at G/FB/Spotify got rejected be a few others.

2. Practice a lot. There are 100s of questions available online. If you're smart, you will pick up the patterns / tricks you can use to solve the coding questions. Eg. when the obvious solution is O(n^2), usually there is a more efficient one involving using a hashmap to do a lookup.

If you think the problems you find online are too hard or stupid (eg. "who cares about implementing an LRU cache"), then read up on core CS topics to appreciate the subject matter.

If you think it's not worth to invest the time to beef up for it, then (i) it is, you can learn a lot at the big ones (ii) you can see how hiring candidates who think it's worth it is better for the company.

3. Think of it as a good thing. You brush up on your core skills (LRU cache), and it probably forces/incentivizes you to look at some recent developments in your sub-field so you feel prepared and can comment on it if it comes up. Although I don't enjoy the interview itself, I find the preparation to be a very fun time, reminds me of the good old days at University; a good break from the usual crunch of the job, which usually leads to rusting of core skills and specializes you in the tools the team/company happens to use.

4. At the big companies, on the initial loops where you solve the shortish interviewing questions, usually they just want you to solve the problem, not talk too much. I found some candidates think they have to talk a lot and relate the problem to their work, but that's not the case. Don't say "At work I'd just use a library for this." That's obvious, that's not the point of the interview. In the initial screens the interviewer just wants you to supply a solution, explain it, and move on. So just do that. Be efficient.

5. Getting rejected feels like shit but doesn't say much about you. It just means you had a bad day, or you were nervous. Or maybe the interviewer actually did a good job of assessing your skills, and you're not a good fit for the team/org that was hiring. I've seen lots of people get rejected from FB where I thought any smaller company would _kill_ to get them onboard, but FB didn't accept them for some weird reason, which at a high level is sth like "Would they be successful here at this role X, in team Y or Z, _given how this role works here_? Maybe, but the hiring manager isn't convinced enough". It's a bit frustrating, but it works for the company: the people who get through the filter are very smart&good, work together very well and efficiently, altogether create products Bs of people use (good for everybody), creates Bs of revenues and Bs of profits. So it works, it's not going to change. Play the game.