Is my lunch hour my personal time or business time?

Can I do whatever I want during my lunch time?

The situation is, I got interrogated by my supervisor who overheard me tell a co-worker that I have a doctors appointment at lunch.

My supervisor says "stuff like this I need to know". He asked me when I made the appointment, how long its going to take, if its a regular check up.

He says "just in case I come back a little late".