I know it's really hard to shake the opinion of somebody close to you, especially someone whose opinion you presumably value, like your Father's. However, I would still stay wear it how you want. This is something everyone has to deal with at some point in their lives, specifically, making their own decisions. God only knows what I would be doing if I had let my parent's decide for me. They wouldn't have wanted to anyway, but still. They occasionally make comments to me about how I should grow my hair back saying the usual "Hair has character" or "you look better". However, I feel better with a clean shaven head and in this matter I am the only person who matters. You're in the same position here.
Also, I don't think this is a matter of whether or not you're paying rent or your living arrangements. The hair is growing on your head and you have the right to do whatever the hell you want with it. Don't feel bad about crying or anything you're feeling now. You're a young man and that has it's own set of unique challenges. Keep doing what you want and what you think you should be doing. Everything else will work itself out.
Good luck to you, Brother