Hey hun, I'm having the same problems as you. Pretty annoying :/ At 29 weeks you should be able to claim income support if your parents stop claiming child benefit. Sometimes income support starts later depending on when child benefit has ceased to be claimed but you should be entitled to it, at the very latest, slightly after baby's born. Also, if you're claiming income support, you should receive a 500 pound Surestart maternity grant so you can buy the main things you need. You should also be able to claim child tax credits and child benefit after the baby is born if you do claim income support.
Put a housing application in with the council and see if they can home you and the baby until you get started. You should also be able to claim housing benefit so the rent you'd pay would be minimal and certainly affordable from the benefits you'd receive.
Have you had information about Healthy Start vouchers or vitamins? You should also be entitled to them regardless of your current household income as you pregnant and under the age of 20. If you don't know about them, they give you 3.10 off all fresh fruit, veg, milk and formula milk a week, and you'd get an extra 3.10 voucher a week after your baby's born.
Also, if you do decide to go back to school or college (or to any course below university level) you would get your childcare costs pretty much paid for by Care to Learn as you are under 20.
Try joining Freecycle as well. You need to have a Yahoo account but it is for people who are giving away free secondhand items on there because they don't want to throw them away. You can post a free ad requesting any freebies that you need and you can scroll through offers to see if any of them are baby item related. I've seen loads of pushchairs, prams, cots, cotbeds, baby clothes, baths etc listed. It's great

I've even had a big bundle of boy's clothes given to me. It's definitely worth checking out and you can't go wrong because it's all free.
I know none of this sounds ideal but being a pregnant teenager is definitely hard :/ I'm just trying to get as much help as possible so I can finish my education and get a decent job to support my baby. PM me if you need any more information; I hope this helped put your mind at ease a little bit. Also, talk to a Connexions personal advisor in your area and they should be able to give you more help (if your local Connexions hasn't been scrapped due to the cutbacks.)