You can't enter Mexico without a pass port at certain times. I believe you may be able to get into Mexico with just your DL and birth certificate. Not sure about getting into Jamaica though. But getting back won't be easy. They usually will not let you back in the US from Mexico these days without a passport, even if you have your birth certificate. You may have to stay extra time at the embassy there also, proving your documentation. Sounds like a mess good luck. I know to get back in the US you do need a passport if you come back from Mexico. Good luck.