I think what the tax preparer was alluding to was common law marriage. I don't practice in Texas but I doubt that filing a tax return for one year would create a common law marriage. The IRS may insist for a time that you are married but the best way to fix that is to filed an amended return for the year in question and fix the filing status from married to head of household or single.
For a common law marriage to exist, the parties must live together, hold themselves out as husband and wife, and there must be an agreement to be married. The agreement can sometimes be inferred by the presence of the other two elements. What the tax preparer is trying to say is that filing the tax returns as married is telling the world you are husband and wife, or holding yourselves out as husband and wife. This can satisfy that requirement. If you were living together at the time, it is very possible that you are now considered married under Texas law.
If you are considered married, then you would need to get a divorce. On the other side of the coin, if you dont want to be married, and your "babys daddy" doesn't want to be married, and nobody ever says anything, then there is a good chance that nothing will ever come of it. You need to understand, however, that by doing so, you may run a risk of seriously complicating things down the road.
As far as child support goes, you should contact the Attorney General's office. They help people get child support.