Hi, I am employment authorization card holder and I am about to get married to a US citizen and giving a birth to a US citizen baby.I was wondering if this could affect my situation on getting my green card. Do I still need to go through the process of getting my green card or just because I married a US citizen would make me a US citizen. I would be so thankful if you could answer my question.

Marrying a US citizen does not AUTOMATICALLY make you a US citizen.

Getting married, makes you married, having a baby makes you a mother, applying with the INS for proper Visa and for citizenship makes you a citizen.

Under the current President it is harder to deport someone who is not in the US legally but married, but he will not be President after a while, so rules change.
You need the correct visa to come into the US to get married even.

A request for a temporary Green Card needs to be made. Then you need to wait a few years and request the temporary status be turned into permanent residence status. Because marriage is an easy way to circumvent immigration and naturalization laws, you will be required to have been together the entire time, and spent a certain amount of concurrent time within the country together.

You can learn more from the U.S. Citizenship and Immigration Service PDF: "How do I help my relative become a U.S. permanent resident"?