Do I have Hemophobia?

Probably not a doc thing as it is an actual phobia. You can check with a counselor if it is affecting your life but many, many folks have this in varying degrees and do just fine. Many of the finest nurses and docs I have known had it in some form when they were young, It is a mind over matter thing. Once you see you aren't badly bleeding or can help someone who is the fear goes away. It'll take some time but if you want to bring an end to this particular phobia you will have to put yourself in the position to see more and deal with it. Or if not do your best to avoid it as well as you can which is difficult as we as humans bleed quite a lot and often. It is a choice but you have lots of time to make it so take it slow.