You should move to an independent room for yourself. I doubt if anyone can offer stay treating you to be a stranger. Your emotions can be understood but someone willing to stay with you without knowing is somewhat scary. Even you would have reservations in extending such a courtesy to am unknown person.
Since you now know what is the reason for your depression, I would suggest you to device methods in shaping your future. For eg., finishing studies, finding a job etc. You are right in your thoughts about no HRT while in PG. Find your individual place and dress up as you like, or share the room with others by postponing your desires to a future date.