Yes! You can easily get a note from your therapist/doctor and talk to the school Adviser and the Resident of Housing and they can make an exception for you. One of my friends said she wanted a dorm to herself because she has had issues with sharing and after and they let her. It took a semester for it to go through but she had no medical condition she was just a brat lol
With proof of your anxiety and the severity of it, they have NO CHOICE but to provide you with your own place. Talk to someone at your school, thats the first step.
Good luck and I hope everything works out for you
and also, congrats on your progress!

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