Honestly? I think you've made the best choice possible. And, no, you didn't fail, because you're a failure. You failed because the plan was to keep the stable relationship and go from there. If you were 26 without a child, you could have made it on your own, barely, and then worked your way up form there, like happens for many. But the child raises the price tag incredibly. That's proof you didn't fail. You love the tyke enough to find a way to survive while young one still has Mom. That's priceless! That tells me rambunctious one will know what love is growing up.
And, God has done more than forgive you. He loves you too. Do not give up, simply because you found some people on a Christian site who aren't Christians. There are two types on here -- Christians and christians. The invisible church and the invisible church. Even Jesus knew which of the ones following him were and weren't his. That's the reality of his people. We have to assume not all who speak know him, even on a Christian site.
If you're a failure, many of us are failures. We had a plan too, and it was working out, until three gallstones and one drop of virus-loaded blood changed our plans. Hubby and I were middle-class Christians with a properly-filled retirement account, when we both became disabled within three years of each other. What we have left is the same thing you have with your three-year-old -- still got each other and Christ. Not failure! Success! The Lord's success.
I've already given you three ways to stop your mom's BF, (he is so not your Dad, even if you've come to call him that), from keeping his paws off you and his comments to himself.
I'm pretty sure you're smart enough to know you need a job to save for a place. Your three year old won't stay three, (which is both sad and good), so by the time you can afford to get out, nursery school, then regular school will help defray the cost of someone watching the tyke, and you can keep affording better. Don't forget, there are rooms for rent too. Since you're just starting to work, you'll probably have to live cheap at first, but as you get more skills and get better at your jobs, you can go on to afford an apartment, and go from there.
You're path turned. Keep remembering that's a good thing, because God is walking with you and bringing you to him. Since he got you at this point, he obviously has plans for you to raise the little one up knowing him too.
Life gets complicated. God is single-minded, and his mind is always on his people with love. Since he's sovereign, this will work out for your good and his glory.
HE promised!