You should have finished your full course at Cozumel without problem - the water is so clear and if you wear wetsuit or "skin" - you should not feel cold at all.
The classroom materials are MUST - you have to understand the theory and procedures then to fully understand the extreme importance of safety procedures etc.
Sounds like you paniced when it came to take off the regulator and the mask - There is no need to panic as a healthy person has enough air in his lungs to sustain short period of no breathing - the reason why it is MUST to be able to handle no regulator and no mask as accidents can happen and would happen - your regulator could suddenly malfunction underwater and you need to switch to your "octopus" - or worse, you have to share a regulator with your diving buddy. Though these days buddy breathing is no longer being taught as most diving operations have octopus (the spare regulator). I was trained many years ago and we were required to perform "buddy breathing" - that is 2 persons share one regulator. Also your mask can accidentally fall off and you must learn to be able to retrieve it and put it back on.
All these maneuvers are very detailed explained in your book and manual - and the teacher also would explain and demonstrate it clearly for you.
Just stay calm and you will master it. The No.1 rule in diving safety is to stay calm - all the things you learned from the book, in the pool, aim at one thing, is to dive safely.
The 2 procedures are important parts of it.
You no doubt have learned about Emergency Ascent - that is when something happened, and you must come up to the surface - many times, you would abandon your weightbelt first, and may be your tank (it could get entangled with fishing net or something, thus you must do Emergency Ascent)...
I sincerely hope you will try again and once you get your Open Water Seacard, a new wonderful underwater world is waiting for you to explore.