Year 3 of Homelessness - Single with 4 Children

I'm 30 with two sets of twins, ages 6 and 2. I've been struggling with homelessness since I was pregnant with the younger 2. It has been nothing but a battle. I receive government assistance, which helps with essentials such as food clothing and occasional hotel. I just got childcare a few weeks ago although my kids can't go half the time cuz they keep getting sick. I would like a healthcare job so I'm saving up for a CNA course that I can do while my kids are at school. However, I'm very depressed because I've tried countless resources with no help. I don't have family help at all due to decades of abuse. It is hard to rent a room with kids. Also, my credit is shit at mid 500s due to living off of credit before I got on welfare and not being able to pay now. I'm considering bankruptcy. My kids attend a great school and it is a sense of normalcy for them so I'm staying in the county.

I'm posting here for advice to get out of homelessness. Ideally, I would like transitional housing as I'm working on getting into a nursing or radiology program for a stable career.

I've tried 211 so many times. Also reached out to my kids schools, the regional center (3 of my kids have special needs, possibly autistic), social workers, etc. I'm just told to call or contact xyz and when I do, there is never a response. Even on Christmas Eve I was on hold for THREE HOURS just to be hung up on saying there are no shelters/resources available. Every resource claims you need a referral but I can't get into contact with anyone for one.

I am seeking any advice please. (No judgement as that does not help my situation)