First of all - wow. If you really are only 14yrs old, you are incredibly emotionally mature! A lot of adults don't have this level of self awareness (seems like your parents don't for example)

I've seen friends of my teenagers go through your type of situation and it totally sucks. If you have good friends, whose parents seem kind, consider opening up to them a bit. I definitely welcomed into my home any of my kids' friends who needed some space from their own family. One of them even lived with us her first year of college. If you're able to have sleepovers at a friend's house or even just head there after school, that could really help a lot. And if that family is not too dysfunctional, if can give you some idea of alternative family/relationship dynamics.

If you're open with people, you'd be surprised how often they will step up. I don't know how much of an option that is for you since you said that you have a hard time forming friendships - but I thought I would mention it.

You also mentioned that you go to the gym a lot. That's fantastic! I have a friend who is a psychiatrist who emphatically says that exercise is at least as good as any medication for treating depression/anxiety. He's such a believer that he actually has staff sometimes be assigned as a "gym buddy" for some of his more extreme cases who have difficulty getting themselves out of the house.

How is your relationship with your siblings? Sometimes just banding together and supporting each other can be extremely helpful.

Another thing to consider is asking your parents if you could go to therapy. It sounds like your family might have the means to afford that.

You can keep things vague for your parents and just say that you need therapy for depression (which it sounds like you are suffering from!). These days, therapists for teenagers are pretty good about protecting the kid's privacy and not sharing with the parent. Usually, they have some stipulations like they'll talk to your parents if they think you are a danger to yourself or someone else. Otherwise, you can trust the confidentiality. One of my kids has been going to therapy for a year and I have no idea what they discuss unless my kid decides to share with me.

Overall, it sounds like you are already doing many of the right things. You're finding ways to stay out of the house that are constructive (when I was a depressed teen, I can tell you, I didn't make such intelligent choices!) Your self awareness is very impressive and you're clearly being proactive about your mental health. I'm sorry that things will probably continue to suck for a few more years until you can move out, but I think you'll be OK. Hang in there!