I am in Cancun. Temperature is in the 90´s with high humidity every day. If I do any activity outside, I get heat exhaustion symptoms. this has gone on for several days and I can´t leave here for another week. I´m worried that continual exposure to this heat may cause other health problems. can it?

Millions and millions of people have lived in heat and humidity like that their whole lives (me included), you aren't going to develop a ton of health problems from it, I promise. All you have to do is make sure you stay hydrated. the heat is only going to cause problems if you don't drink anything, actually come down with real heat exhaustion, don't do anything about the heat exhaustion, and then continue to not drink and stay outside anyway. then you have a heat stroke, and those are bad. I have a family member who got permanent brain damage from that, he's never been the same since.