Finding Doctors in Cancun
Not only does Mexico have four medical schools in the world's top 200, but the country also attracts talent from other countries. You can get very good treatment here and it is generally very affordable.
If you've got something urgent and it's not mysterious, you might head to Cruz Roja on Yaxchilan in SM 21, not far from Sam's Club. You register outside at the service window, take a seat and wait your turn - of course, by triage guidelines as you'll have given the reason for your visit. Probably best if you're with someone who speaks Spanish, but I think it is not necessary. At the end, you'll be asked to pay something like 50 pesos as the suggested donation for services - but please remember that's a suggestion so that anyone can afford it, and it would be appropriate to offer more, to support their good work. Their phone is 998 884 1616, but you should just go directly there. For emergencies, call 911.
But if you need a good diagnostician, choose a specialist. I've had very good luck using the free Directorio Médico de Cancún: I just look the doctors up online, choose by medical school and certifications, and usually get an appointment within a day or two. The other option is to head to a hospital and register with their Urgencias - Urgent Care - where you'll get to see a specialist within a reasonable time. Of course, I've also asked Mexican friends for recommendations of doctors in private practice, but some of them have been booked too far out for my timeframe. In any case, note that many doctors in Cancun have evening office hours; it's not a 9-to-5 world at all.
On the other hand, I do not recommend trying the (usually free) Consultorios attached to pharmacies. I'm not going to tell stories, I just assure you it is a far cry from the fine care you can get by following my suggestions. It is tempting, so convenient, and Mexican friends may tell you that's the thing to do, but: no, it really is not.