I know this is a very stressful time, so I would take your problems as they come.
What do I tell my baby when he/she grows up? Right now thats not an issue. Forget it, cross the bridge when it comes. And when the time does come, you will know what to do.
Will only my name be on the birth certifate? Still a little early in the game, but you need to find out what your state laws say. You weren't married so you may not have a choice. (check this out for yourself)
Im 12 weeks and Im so emotional about all of this and its hard to take in. Take care of your pregnancy, its your number one concern. Build a support group. Read up on things (What to expect when your expecting, The Complete Single Mother are GREAT books to start with)
So what now? Build yourself up emotionally. You will need it, and yes....seek Child Support. Seek out resources. Sometimes churches have support groups, and even your states Child and Family Services have groups that meet up. I found groups even at libraries! Make this a positive experience for yourself and your child and what better way to start than now! Believe me it will get harder, its you attitude about all of this that will determine the outcome. Not sure if any of that helped but its what got me through the tough times. Good luck!