I got my place after my first child was born. I would say (based on where I live only) that at this stage of your pregnancy, you'd not be offered more than a one bed though and depending on how the system works where you are you may be more likely to be offered a bedsit or similar accomodation in an emergency situation over a flat or house.
I would say go and speak to a housing officer and explain your situation in some detail. I think they get a lot of stories so sometimes can be quite harsh with their decisions, but if you explain how difficult things are at home you should get some help. They can do a lot if they want to, Good luck!