Take it one day at a time, Amy. 
It will honestly get better. I think you're being so strong, going to the doctor and arranging counselling when you feel so much pain. Well done!
I don't know how serious the problems were that led to the break-up but whatever you may have said or done when he upped and left, people KNOW that we all behave differently under that kind of pressure than we do in normal life and won't hold it against you forever.
I think part of what makes all this so very hard is that you are also living in a military environment. I imagine that it is very cliquey and that dh's workmates and their families will side with him because of that. It's not because they think you are so awful, honestly I don't think so. It's like a big club, isn't it? And since dh left, you're like an outsider living on club grounds. No wonder you feel so down.
It makes it especially hard for you to be there with your little one, feeling the way you do, with everyone siding with ex and against you, that's why I think it would do you good to get away. I can understand you don't want to go to your parents, if mum is at work all the time and you don't hit it off with dad. That would just drag you down more. Is there someone else you could visit, even if it's just for a weekend, to get out of that environment?
Are you sure this break is final, Amy? Lots of couples go through a major crisis when they have small children, it just is such hard work. What were his reasons for leaving? Were you happy with him until he left? Was the marriage and the whole situation fine for you?