Sorry, not exactly feeling great myself but didn't want to let this go unanswered.
Firstly, try not to panic. It's really hard when dealing with the emotional fallout to also look at the practical aspects but these probably need to get sorted first. Given that it is now Sunday and you'll be unable to do anything before Monday, you can look at entitled to (tax credits, housing benefit) and the CSA website (child maintenance) which should give you some idea as to what you would be entitled to.
Secondly, try to get a good night's sleep. Hard I know, but things always look even worse if you're tired.
Thirdly, try not to panic. I would really suggest that you don't try to make too many decisions at once. They say when you are grieving not to make any major decisions in the first 6 months. Well, you are grieving for your lost relationship and that will take time.
Then you are left with the things you know. You currently have somewhere to live and a lovely DS who needs you. Believe me, in the first few days and weeks, he will be looking after you. You will have to get up when he gets up, feed him, look after him, take him out etc etc. Just concentrate on this for the moment. Decisions about where to live etc come much later.
My DCs are too old for me to know much about it but Sure Start seems to well rated on here for offering support to mothers of young children.
Hopefully others more together than me will be along shortly.