Is it normal that i'm afreid of mental hospitals

Ever since I discovered what that huge gray-white cement building was, with spikes on the walls. I'm scared of insane asylums, not because they're terrifying, but because of the fact that as soon as you put your foot inside that building, your sanity is in doubt. How long have I been here? What did I come to? These are the questions that constantly come up while I do not take my eyes off the doctors. The fact that a doctor simply says you're crazy, would be enough to get you there.

I never went to a madhouse ... and I never wanted to go.

I ask if it's normal, mostly because I did not find it with a specific name like agoraphobia or something like that. What do you think? What should be called the fear of asylums?