Most likely you would be hard pressed to find a place that includes utilities. The reason is the apt management would not know how much power you would use if you like air conditioning.
If you figure your rent would run between $400-$500 a month
Your grocery bill will run you about $50 dollars a week (might even squeak in a meal at a restaurant)
As for health insurance because of your age, and preexisting condition you only choice MAY be the public health system.
*I have no direct knowledge of the cost, but have heard it runs about $300 usd's a year.
*You need to check to see if you even qualify without a Temporary or Permanent resident status.
You also need to consider what the cost of Internet, and TV would cost, if not included in the rent.
Transportation costs, Taxi, bike or walk. The cost for taxi's depend on where you live, and how often you use them.
On a Tourist Visa,( which is what you said you would have) you can request 180 days on the island, then you need to leave Mexico.
To net it out, you can make it on 2k, but your going to have to watch your budget when your electric bill comes due (every 2 months).