Will i be able to get housed by the council?

i have just split from my partner, as it has become unsafe to live with him anymore. We have a son who is 2 and jointly own 50% of our property - the other 50% we rent. Me and my son are now staying at my parents - 50mins away from my work and my sons playschool - they only have a one bedroom bungalow so its a little cramped. I only work 16hrs so will not be able to afford a place by myself. We are looking to sell the house but its takes time and my partner pays the mortage side so he will not leave until its sold. I am really stuck as have not got a clue where to go and what to do. Its too far from our lives to stay at my parents - and theres just not the room. I hope someone can help - even if its not what i want to hear!