You sound as if there is far too much in your life for anyone at all to cope with . You go to work - which is extra busy, your husband is an alcoholic and probably eats up the finances, as well as making uncalled for decisions,.
New town, no family, no one you trust, schooling problems, health issues and feeling used as a domestic and for sex -which you don't want. I'm not surprised you went to the doctor.
However from your account I'd not even be sure treating you is the most appropriate thing. Maybe in the short term in case you become overwhelmed (Sophie has given you some good numbers to call) , but in the long term?
I noticed you said
"I know he is sick and I don’t want to walk away but there is only so
much I can take and I have to also think about our children and the
damage his behaviour might cause them."
This is sensible stuff, so rather than wade in with suggestions that may or may not fit may I ask you what you would like to do?
I know that is a difficult thing to ask and you may not know the answer - whch might be where outside advice might help. The alternative from what you said might be stay put in the current environment, leave and maybe return to near your family, or what?
Can you talk this over with someone you do trust and cares about you?
I hope to hear from you soon