Dude, I mean no disrespect. My on child, who suffers from a similar issue (though of course it isn't the same, and your child needs individual treatment, and deserves that), really benefitted from a team sport. It didn't involve his parents, he had to play by certain rules, those rules were enforced by adults who are not his parents. All these things were huge advantages. I'm not suggesting it works for every child, but team sports can be a very positive thing for kids with these issues. I coach hockey, and I have dealt with kids who are biters, fighters, and any other negative social thing you can think of. Getting them on the ice, or on the soccer field, or on the basketball court, or whatever can be fantastically rewarding for them with the right coach.
In any case, no matter what, know that you are, in fact, a good parent, and this is not something you can fix by just loving your child. It's going to be a life long journey, so accept whatever help you're offered.
Honestly, you're doing a good job. Start every day there.