Generally, it is preferred to have your hair tied during a check up just to avoid any hiccups during any point of the examination that might be uncomfortable for both you and the patient. But if you have very short hair, and they do not usually cause any botheration, then you can leave it down. It also depends upon the type of check up being performed. I am a doctor and I prefer to tie my hair if my check up requires movement on my part and interaction where I know my hair can cause any kind of issue, small or big. With that said, when I have to do rounds or follow up, my hair is usually down and I like it that way :D. I think you just know according to your situation. If you really like to keep your hair down. just keep a hair tie with you on your wrist at all times. It is not a very hard and fast rule but it is frowned upon mostly as far as I know.