Rosalia asks, "I came last week to marry my fiance who is a green card holder, hoping to return home and wait for consular processing of I-130, but I noticed that in the meantime the priority date became current and now I am tempted to stay and apply for adjustment of status here in the US. Can I do this?"
Indeed, you can, because you were lawfully admitted to the United States. Since this is not a straightforward case, I strongly suggest that you try not to do the paperwork yourself and get a good immigration attorney. You see when you entered the United States, you intentionally came for your wedding and generally that is not tourism, the main purpose of the visitor visa. The USCIS officer reviewing your application is going to be very skeptical, scrutinize your application very carefully, and might even reject it if he is not convinced that this is not a sham marriage. If you are rejected, you can still apply through consular processing (CP) but if your lawyer files your petition with all the paperwork in perfect condition, you will be able to live with your new husband and not be separated.