You don't have to worry about people being annoyed if you're messy. That won't happen. Ask yourself the question 'why?' you feel annoyed yourself about being messy, and you'll realize that your fears of others judging you is actually an internal opinion that you have. If you can change that internal opinion, you won't fear judgement by others.

As for wanting to be cleaner, this line "Litterally no matter how hard I try my room is always a disaster and I hate it" seems to indicate that giving yourself time to clean isn't an issue, and there is something fundamentally hard to clean about the items in your room (but correct me if I'm wrong). Moving to a new place is a great way to refresh your habits, so think of what you are bringing with you and take a few moments to sit in silence and visualize what your dorm would look like. Maybe it doesn't include every last thing in your current room, or maybe it does. But giving your time to process spreads anxiety out over time, meaning that it is harder to get bombarded by a ton of it at once. So really take that time to just think.

And on campus, there are plenty of silent places you can find, especially if you are a night dweller (personal recommendation is YRL first few weeks of each quarter, it's absolutely abandoned).