Well, I think we've loaded this thread with enough feedback and commentary to freak the OP'ster out (myself included with blood pressure commentary). I know I'd be freaked out if I read through all this as a new diver heading to Mexico for first dive trip and my BP would be through the roof.
Cutting through all of this, the OP stated he was going to do a reef dive on the mainland followed by several cenote dives. I agree with a prior post that stated cenote dives may not be the best UW environment for a new diver. I would recommend this diver pay the few extra bucks for a dedicated dive master for his initial reef dives on the mainland and further recommend that he consider doing more reef dives on the mainland until he is comfortable with his buoyancy and has listened to the advise of a DM who can give some instruction on how to minimize air consumption UW. A few cenote dives could then follow if he is totally comfortable and either sticks close to the DM or again hires a private DM for initial cenote dives. Vacation is supposed to be stress-free and I say if one is stressed about a dive, spend the $ and hire a personal DM, relax, and enjoy yourself. Skip a few dinners out when you return from the trip to save the $ you spent on the personal DM.
Once on the island of Cozumel, I'd recommend a private DM again for the first day as this will be new drift diving. A private DM on the island runs about $50 bucks for a 2-tank dive and there is nothing better than having your own DM who not only can provide instruction and watches out for you but can take you on a tour and point out critters 99% of us pass by never knowing they were there. Again, after becoming comfortable (and it usually won't take but a day of diving with a DM) the diver is comfortable and ready to dive the rest of their trip.