I stayed at home when i had my son, but my dad went and enquired about where i stood with housing, because of my age they could only put me in a hostel till i was 18.
I didnt want to leave anyway, i moved in with my Bf, and his mum when i was 17, and i put my name on the council waiting list. I got my flat when i was 18.
By that time i had split with my Bf, i went on benefits, so my rent and council tax was paid, and i recieved an amount each week, and child benefit every month.
Once my son went to playschool when he was 3, i found a part time job.
I would suggest, if you have decided to keep your baby, make an appointment at the CAB, they will be able to give you all the advice you need.
Also go to your local council and look into putting your name on their housing list.
Remember, there is no shame in using state help when you really need it, you can also get help now with courses and childcare, so you can still have the career you want.
Good luck.xx