Not always easy, but there's always a way.... and I think that the amount of difficulty to getting work and residency visas also varies based on what what you're doing, who is sponsoring you, etc.
I don't have personal experience doing this in Mexico, but elsewhere my employer had to fill out paperwork stating they weren't able to find an better qualified citizen or work-eligible legal resident to fill the position.
Your trauma and ER nursing should be a big plus for you.
I would guess fluent Spanish will be a requirement and any other language would be a bonus too. You might not get into a hospital, but maybe a doctor or clinic who gets lots of tourists and ex-pats could be a possibility. In Cozumel or Playa, having some dive medicine training or being a chamber tech would also be a huge plus. Tropical diseases could be good too.
If it's something you really want to do then go for it!!!! Start doing some networking to get connected with people in the medical community there and find out from them what your best options are for making it happen. Might not happen instantly but don't give up.