I think the main thing is that impersonating someone and using their information to get a job is called FRAUD and Identity theft and is illegal. It doesn’t matter if your GF says it is ok. The other thing is, unless you have authorization to work for a US company and the required visas, this is also illegal. These are 2 potential state for federal charges that you can get if you are found out. That could lead to consequences as a fine, jail, barred from entering the US. You need to reconsider this approach.

You need to talk with a Mexican Immigration officer to find out how you were processed. And go from there. Just because you went there intending to go on a 180 visa doesn’t mean that they can’t place a time restriction on how long you can stay in the country.