I can tell from your letter that you are a very sensitive person. The upside of that is that you are probably insightful and sympathetic about lots of things. The downside is that you are still learning how to manage your own sensitivities. On top of all that, you are at an age when you are adjusting to changes in your body and your hormones. All this can make things loom much larger than they need to.
Meanwhile, your dad is adjusting to the fact that his little girl is growing up. He’s not used to having a young lady in the house who is experimenting with her looks and who is asserting her own individuality. Because your mom was once a girl, she is more likely to understand.
The mature thing to do is to stop isolating and start talking. Start with your mom. Talk with her about how much your dad’s comments really do hurt. Ask her to help you talk with him about how important it is for you to try out making some of your own decisions and to try some new looks. Let him know that his opinion really does count – a lot! See if you all can work out a way to have differences of opinion without name-calling. Meanwhile, get out of your room and do some fun things together as well. Share a game, introduce them to some new music, make dinner together. Positive times will help balance the more difficult ones.
You are adjusting to being a teen. Your parents are adjusting to having a new teenaged you. It’s normal for there to be some bumps in the road. Focus on how lucky you are to have folks who tell you they love you and who are trying their best.
I wish you well.