"FAFSA" is not an organization. There's no money from "FAFSA". The FAFSA is a *form* you fill out, a form created by the Federal government, to determine financial need. It's not a promise of money. I'm explaining this because it's like saying, "I got a speeding ticket, I'm going to complain to the DMV office because they gave me a license!"
So, that said, you're an independent student if are any one of the following:
Are you 24 year of age or older?
Are you married?
Are you enrolled in a master or doctorate program?
Do you have children who receive more than half of their support form you?
Do you have dependents other than your children or spouse who live with you?
Are you an orphan or ward of the state?
Are you a veteran of the U.S. armed forces?
So, it's not enough that you have a child. That child has to get more than half its support from you. If you and your girlfriend had a child, but that child lives with her, and you don't pay more than half the total expenses, then that child doesn't count. Additionally, you can have a girlfriend, but if you're not married, that doesn't count.
Anyway, what it sounds like is that the school did a verification on you and found that your independent status could not be verified. Based on what you've said, that makes sense. Do you live with your girlfriend? Who pays the rent? Who pays for food? Are you living alone, or with your or her parents? Does this baby like with you both?