It's great that you're going to see a doctor. It shows that you're aware that something isn't right and you want to take steps to fix it. Remember that the things you have been thinking or doing, such as self harm, are nothing to be ashamed of because they are a part of a greater problem. In fact, you should be proud that you recognize that these behaviours aren't healthy and that there might be an underlying cause for the way you're feeling.
It's very scary to let our loved ones in on how we're feeling. I still don't go into great detail about it with my parents. They're supportive, but it's also difficult to tell them that I'm unhappy and there's little/nothing they can do about it. Please, please make telling the doctor EVERYTHING your priority. He won't be able to help you unless he has all the facts, so do what you have to in order to give him what he needs, even if that means asking your dad to wait outside. I've kept things from my doctor and counsellor and have only made recovery much more difficult for myself. If you are uncomfortable talking to the doctor in front of your dad, ask him if he'll wait outside while you have your appointment in private. Make sure that you stress that you appreciate having his support, and that you do want him there for the comfort of knowing you're not alone in this. It might make it easier on your dad that way. Good luck!