Heartache hurts. Loneliness makes the hurt worse. Being "different" makes it worse from there.
Maybe what you need to do is stop. Just stop everything.
From what I've read, you don't have anyone for YOU. You dad isn't there for you, he's there for his own reasons. That SOB who hurt you? He's not there for you either. Nor is your mom or your social friends. Not even your new playmates because they're only sharing themselves with you.
In all of this, who is really caring about bunny when she needs someone? Who brings you chicken soup because you're sick? Who leaves a mint on your pillow for you just because? Who sends you an envelope full of rose petals in the mail? Who calls you just to say hi and listens to you breathe because you don't need to actually talk for them to get you? Who reaches out to you to just hold your hand when you're together?
Time to stop all the nonsense. Go out and find someone for YOU. Just for you. Get into that "it's just lunch" thing and go meet some people. No pity sex either, NOTHING in the prior paragraph I just wrote had sex in it so don't go there. Instead just do lunch. Have a good time meeting new people, maybe making new friends who might be interested in bunny enough as a person to come to her B-day party.
Life is about living, not enduring the crap others throw at us. Take a deep breath and go find someone for you. Just for you.
I don't particularly care if you don't like it.