Hi Purple,
I'm also a single mom without insurance. I just recently began therapy through a community health center. I applied for something called MHDD and was given 33 sessions for free. You could call around and see if there is something like this in your area. I'm not 100% sure, but I think they also told me that when my 33 sessions run out, I can continue to see my T, using a sliding scale fee.
I can really empathize with you; being a single parent is rough.