i dove the cenotes thru Tank Ha a couple decembers ago. good dive op, there was a german DM that was very precise (imagine that). the cenotes are amazing btw, like being on another planet, but given your number of dives and your nervous feeling i would agree with the other posts that caution you against it right now.
they are not considered caves because technically every 50 - 100 feet there is an opening, but in reality when you get down there, everything is dark and i couldnt tell where these opening were at all. an OOA situation would have been trouble, especially b/c we were not outfitted in proper cave diving gear with doubles, alternate sources of air, etc. someone died in a cenote the week before i dove. i dont know the details.
once you're more comfortable, tho, i think they're one of the most amazing dives out there...
re the weather, it was sunny then it rained, then sunny, then rain, etc...great italian food in playa del carmen too...
hope this helps you make a decision.