Hugs to you-- hang in there and keep pushing yourself to get out and talk to other moms. It's great you joined the groups and you just have to go in there with the thought that everyone there has good days and bad days and you all want to support each other. Also, keep trying to get in touch with the counselor. Even though the place said they don't deal with "serious issues" call them. If moving to Florida with your support people is an option, I say do it. Can someone from Florida come and stay with you for a few weeks?
I have a history of depression and anxiety, so it wasn't surprising when I had PPD with #1. It wasn't anything really serious, but I did become very withdrawn (socially -- I am actually a very social, people-person type, but I felt too anxious and depressed to get out and do anything or ask for help) and had to go on medication. With #2, things took a different turn. I was more anxious than depressed and basically did have a breakdown (drs diagnosed me with "post partum psychosis"--yes lovely label.... Turns out I'm acutally bipolar, but that's a whole 'nother issue!) So, I know exactly where you are coming from right now.
My "breakdown" occurred right around the holidays when my dd was 4 months old. I was exclusively bfing her and didn't want to be admitted to the hospital. My husband's a medical prof. and works very long (often overnight) hours. So, I am mostly alone w/ the kids. Both of our families lived thousands of miles away. His family was able to come out when I became very ill to help care for the kids. If that wasn't an option, I don't know where I would have turned-- perhaps to a friend or member of our church? So, I didn't want to be admitted to the hospital, but there also was no place for me to be admitted (unless it's a life threatening emergency or you can pay alot of money for a special, private facility, the beds are very limited). So, I was sent home w/ really heavy meds and mostly slept for a few days. After that, I went to and outpatient treatment for a few weeks. That was really helpful because it allowed me to stay in my home (w/ the kids), but also get the help I needed. Since the outpatient treatment was at a local hospital, I'd imagine I could have arranged for some sort of child care if I needed it. Maybe they have something like that available to you?
I don't recall if you were taking any medications. A primary care doctor can prescribe some basics and maybe they could help you get in touch with the right therapist or psychiatrist too. I'm not a med pusher by any means. It was not something I wanted to do at all, but it was something that saved me.
To finish out my story... I will tell you it's been a long road-- it was a very difficult 2 years after dd#2 was born. Through alot of therapy, faith, and working with my family and friends, I could finally say I was "better" Now, 6 years after my "psychosis" I am med free!! I could never imagine i'd be able to learn so much about myself or use these new skills to improve my life.