Your not useless Lee, you're a Mother.
You have a little guy depending on you to be his world right now- beating up on yourself isn't doing either of you a world of good. Everything is about him so make it your priority to be be the best Mom you can be. Better yet, give him a reason to be proud of you years in the future when he looks back and realizes that your love for him brought out the best in you.
Hopefully you've made an attempt to pursue child support. If not, get on it. Pride isn't going to pay your bills or put food in babies mouth.
The relationship with your former partner is gone. Don't agonize over it, better to find out now than years in the future when he's a deadbeat not taking care of his family. Hopefully you'll be more demanding of quality in the future when you find someone you'd like to be with again. Don't rush into anything else- put the little guy first.
Don't give into despair Lee- you need your strength and to be upbeat. I know nothing of your education, possible career, financial situation, or background. Regardless of how good or not good it is you have to remain upbeat for yourself and baby.
I have met many single Moms during my time on the earth. I respected the ones who made sure that baby was taken care of first, I never respected the ones who had to make everything about them and baby got whatever was left over.
I sincerely wish you and young mister luck- its a real privilege you've been given caring for him. I speak from the heart- my 9 year old daughter is the absolute center of my world, nothing else has been more important to me than her well being.