Do you own a tent? You said you live in a southern state, so living in the woods in a tent may be an option for you. If you don't own one, maybe you can get a used one cheaply. As someone else mentioned, insulation from the ground is key. You may want to try to get your hands on an insulating camping pad, or some other similar material. Anything to help insulate from the cold, wet ground. You also may want to look up how to make a debris hut, which can provide an insulated shelter and potentially save you from hypothermia in cold conditions. In terms of a blanket, I would try to get a wool one (try military surplus stores), which are heavy, but very warm, very hard-wearing, and retain their insulating abilities even when wet. They also won't melt if they catch a spark from a campfire like a blanket made out of synthetic materials will.
There are forums and blogs for homeless people (don't know any off hand right now, but I have stumbled across them before) where you can probably pick up tips. If you do want to live out in the woods, you may also want to look up videos or tutorials about DIY outdoor gear and bushcraft skills, like building basic shelters and making pop can stoves.
I'm sorry you're facing this difficult situation, but the more information you can arm yourself with, the better. There is someone in my area who lived in the woods half the time by choice, and he often would run into homeless people. He tried to teach them basic skills like making debris huts, but apparently they weren't interested for the most part. These are skills than can save your life though.
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Not all those who wander are lost... but I generally am.