If I marry my girlfriend and she is a 19 years old US resident can I still apply for a green card?

If she is a US citizen and you are legally married under the laws of the state where you got married, then she can petition for you and you will be immediately eligible for green card processing. however, if she is only a permanent resident, she can petition for you but you will have to wait until the priority date is current to apply for the green card. Furthermore, you would have to be in the US in valid status and not an overstay in order to apply for adjustment of status once the priority date becomes current.

Since you are already out of status, you are no longer eligible for adjustment of status in the United States unless your fiancee becomes a US citizen first. Otherwise, she can only petition for you and you will need to return to your home country for the visa interview at the US consulate. If you overstay by at least 6 months by the time you leave the US to attend the visa interview, you will be subject to the 3- or 10-year bar from returning to the country and must file a waiver in order to come back. It may be a better idea for you to wait until she becomes a citizen before filing your paperwork.