I guess it is good that you are not alone in your fears, that you and your fellow classmates are all human with the same fears and desires.
For me I have rarely felt anxious about writing anything because I mostly just write for myself. But I can see how the pursuit of perfection can cripple the creative mind.
By bad writing do you mean poor spelling, sentence structure, and grammar? Or poor writing as in it reads like something a drunk donkey typed out on a treadmill machine?
Haha, I guess both! For me though it's more that I try to get everything "right" in the first draft, and I tend to edit as I go, which isn't the best way to go about it. It's important and easier in the long run just to get it all out while you can and then go back and fix everything up. For some reason it got in my head that if it wasn't a masterpiece the first time around there was no saving it, which is far from the reality of the situation.
I tend to write mostly for myself too (although I'm obviously working on that changing!) but even then I feel this internal pressure. It's really silly. For example right now I have about three short stories I'm working on, and just knowing that the documents on my computer are messy and incomplete makes me feel very uncomfortable.
By the way, I really enjoy the stories you post on here.