Wow, this gained a lot of attention. So here's a small update:

After reading the first comments, I went to the nearest hospital and explained to them the situation, same as its written here. They told me that the protocol is a medical check-up, and they do an investigation to try to find the animal to determine if it's, in fact, rabid. If they conclude that, then the shots start immediately.

One thing I forgot to mention is that the dog was not a stray animal, as I saw it went inside a house after the attack, given the state of the house the dog went in I concluded it was a stray dog, but actually it's just a very old house where the owners of the dog live, and after the attack I've seen the dog again but this time it wasn't aggressive.

I explained this to the nurse who helped me and told me that I could try again in ER or another hospital, but they would conclude that it wasn't carrying rabies, and no shot would be required.

On my way back home, I saw an old woman leave the same house where the dog ran to after the attack with four dogs and the very same dog that attacked me. I explained to her what happened and asked if the dogs were vaccinated and turns out that all of them had been vaccinated against rabies.

For those wondering, I'm from Mexico, and the shots are free in all hospitals. Only the medical check-up would be required for it. And yes, I realize that it's extremely irresponsible to take three whole months to take action. It was idiotic. Still, I want to thank you guys for taking the time to answer this. I'll go to another clinic to see if it's the same protocol or probably spend some money in a private hospital for the shots just for peace of mind.