I face the same anxiety at times, especially the part where it wouldn’t go away even after I’m done. I’ve started trying something and it’s really worked, since I kept feeling stressed even after begin productive what I do now is write up a list of everything I need to get done with. After I finish it, I cross or tick it off the list, and this physical action of actually marking something as completed helped my brain accept that I was productive and managed to be done with work, which in turn eased my tension. Try it out and it might work for you too!
Also, always give yourself a chance to take a break and pause for a minute. If you’re continually in a rush to do things and don’t give your mind and body a break to relax, it will make you develop prolonged anxiety and even make your muscles tense. For example, you can work for 60-90 minutes, and then take at least a half hour break to maybe get a snack, watch or read something you enjoy, take a nice walk outside, talk and hang out with a family member or a friend, etc. And then you can go back and finish other work.
One last suggestion I have is sticking to a schedule; try to decide ahead of time what you’re planning on doing and for how long. The earlier you start working on something, the more time you have which gives you a better chance of taking it easy and not feeling like you need to rush through everything.
I hope this helps. Best of luck! And don’t worry, what you’re feeling is completely natural and happens to virtually all students.