I have no idea what you mean by special housing accommodation?
You research the cost of living there and identify an area - allowing for a decent school with available places. If it's affordable, you get a job there then rent a flat at the same time giving up your tenancy where you are.
Or if you're in a housing association place, you recognise how valuable that is, and you look for a swap.
If you have your own house, you could let it out whilst you rent in the new area.
Or you could expect your boyfriend to be the one that moves - and consider that if he won't, perhaps he's not worth you moving for.
Or you decide to only move for a serious long term committed relationship, and you just wait it out until you're ready to live together.
Or if your child's father is local to you and properly involved, you stay put and suck it up for the good of their relationship.
So there's a few options for you. But bottom line - there's nothing special about moving, people do it all the time! Be careful it's not you making all the effort though.