My new stepfather, a U.S. citizen, is applying for me to get a U.S. immigrant visa (a green card). I am now 15 years old. But my mother says I don't have a birth certificate from when I was born. We are going to try to get one now. Will this work? I'm scared that my mother will get to go the United States and I will not.
What you are describing is often referred to as a "delayed" or "late-registered" birth certificate. It can indeed be accepted by U.S. Citizenship and Immigration Services (USCIS), although this depends partly on what country you are from, why the birth certificate was unavailable in the first place, and whether you have any other, "secondary" proof of your birth.
Do you know why your mother did not get a birth certificate for you? In some instances, parents who live in remote or rural areas simply can't afford to go into the cities where the appropriate government offices are found, in order to do the registration. In others, birth certificates are simply unavailable for certain time periods or due to certain events, such as fires at a government office.
If birth certificates are known to be unavailable to people born at the same place and time as you, this will raise the likelihood that USCIS will accept a delayed birth certificate for you. To find out the U.S. government's opinion of whether your mother should have been able to get a birth certificate for you, see the U.S. Department of State's so-called visa reciprocity tables, choose your country, and check the entry on birth certificates.
Even if there's a good reason for you to lack a birth certificate that was issued around the time of your birth, however, USCIS is always on the lookout for fraud. There's a good chance it will ask you for more information, such as sworn affidavits from your closest family members, school and medical records showing your name as well as your mother's name, and so forth. If doing so won't hold up the process, your U.S. petitioning stepfather might want to submit these along with the I-130 visa petition. Otherwise, you can wait until the U.S. government requests such follow-up documents.
If this becomes an issue in your case, it would be worth hiring an immigration attorney to help.