I really don't mean to be scaring you about Cozumel diving! It really is fantastic, but it takes a bit more attentiveness to your depth gauge, your air gauge, and your DM. They really should not be dropping you on a reef with screaming current. Most cruise ship divers have less experience, so they are more work for the DM anyhow. Last thing they want to do is stress out divers and DMs.
here is a little sample of Cozumel diving.... NOT cruise ship diving, this is from one of our week long vacations to Cozumel. We dive there regularly.
the shallow reef, with tons of fish, is Paradise Reef. It is 30-40' deep and the closest reef to the cruise ship docks. It is almost always going to be the second dive for cruise ship divers. Can have a little current, but it is shallow enough not to be a problem as long as you stay with the DM. There may be 3-5 other dive groups on the same reef (it is popular second dive for everyone) so make sure you don't start following the wrong DM.