thanks for your question. it is relieving for me to see that I am not alone in having questions such as these.
in my own experience i felt quite blocked, and particularly tense and ridden with anxiety (although i wouldn't have called it that at the time) when i was writing essays. In my experience, and interpretation, I think I was trying too hard to be concise (akin to concentrated) to get my point across. I could not flow easily in my essay writing. This may also have partly to do with a fear of criticism, and not being given room to make mistakes.
I think I did a lot of damage on the way to resolve these issues. So my first advice would be to take whatever approach you do slow and gradual. Sometimes settling into whatever your process is, removes the pressure you have to feel, esp if the case is that you are trying too hard).
Examine what you think might be causing you the anxiety? Do you write on your own about topics? Are you more comfortable writing something that is not going to be examined or marked?
Perhaps you also need more time for the material you are writing about, to be digested by your brain after you read it. Or perhaps you need to plan better. Perhaps the pressure is a result of the brain grasping at the material you have just read and trying to piece it together. Maybe you need time and repetition to internalise whatever you are writing, so when your words come out of you, it is coming from a steady, stable place inside of you.
I am wondering - does this pressure feel like you are trying very hard to focus, or does it feel like you are pushing your focus out - as in pushing words out too? In the past I have confused creativity for reactivity. I think this is often done in the art world. Often, people can come up with all sorts of words and such, in a short period of time, and it looks impressive. However, if you look at the quality of the words, they're often quite poor. Concentration is important here.
I am also wondering - how easy you find it to sit long periods to read or write? Do you find the build up of pressure overwhelming? Can you read for a long period of time?
Perhaps your thought is too concentrated to be comfortable. Perhaps you need to learn to sit and choose an anchor.. like your breath, and/or learn to use a little less effort. I think this is a dangerous term ppl (incl myself) misinterpret what it means to relax your attention. Personally, I find when my attention is more relaxed thoughts and words flow out more. I'm not sure if this is a good or bad thing, but I think it helps with conventional studying.
Often in a university or school setting, we take that organisation to be the authority, and if we cannot conform to those standards, then we think there is something wrong with us. I often think that the school system can do a lot of damage. People are encouraged to have an opinion about everything, you are encouraged to read (I don't think reading is bad, but the way my schools went about it had a lasting negative impression on me), and things like exams and cramming, can put a lot of pressure to the mind, in a way that feels quite 'unnatural' and possibly harmful over a period of time.