I'm 22 from Dallas and my son's mother didn't put me on the birthcertificate, I take care of him the majority of the time as she only has him 1 or 2 days, every other week. How do I go about getting my name added to the birthcertificate, and how would I go about getting full custody of my son, I know it's nearly impossible for a father to get 100% custody but I'm shooting for the stars. I want her to be in his life and for them to have a relationsip, however, he is 18 months and she has yet to provide either financial responsibility, adequate daycare, or a suitable babysitter.

Words, full custody, 100 percent custody, so often can mean the same thing in some areas.

You already have physcial custody, since you have the child, not legal custody. You need to file for custody, get a DNA test to prove you are the father and prove you are the primary care giver of the child.
Then the mother will get vistitation and pay child support.

You can go to court for a paternity test with a request for being added to the birth certificate and full custody. It is hard to get full custody unless you can prove abuse/neglect. You could go after full custody or joint custody, most likely ending up with joint.