"Bless you, you sound really strong, despite the people who should be giving unconditional support all actually letting you and the baby down.
My god. This is your first pregnancy. You're only 22. And your mum is horrified she might have a baby in the house. And your bf needs 'another month or so' to agree to live in a house with you?!
Absolutely rent your own place. Do your own thing. Be the adult you clearly are (well done 💐). You sound like the only adult in all of this!"
This with bells on. You sound bloody amazing, OP. So grounded and sensible. I'm more than twice your age with two teenage children and I'm pretty convinced you're already more mature than I am! I'm sure you will do a terrific job of parenting also, including if you end up parenting alone.
Not RTFT so not sure if it's been mentioned: there will be a question around whether or not you should register your flakey BF as the father (since you're not married, you wouldn't be able to do this without his consent or a court order in any case). This is relevant because he will automatically have parental rights if you register him as the father. If you don't, he won't automatically have those rights though he will be able to apply for them.
You're still early on in the pregnancy so these considerations are several months away. Hopefully, by then your BF will have got a grip and proven himself to be a responsible partner and father-to-be. However, if he has still not stepped up by then, you may decide to go it alone and you may not want to give him the benefit of automatic parental rights by registering him as the father. Just flagging the point in case it becomes of interest to you in the future.
Good luck, OP! Based on what you've said so far, you'll get on top of this situation and make a terrific mum.