Excellent medical care is readily available, but the need for medical insurance when visiting anywhere in the USA cannot be overemphasized. Doctors often expect payment on the spot for services rendered, after which your insurance company may reimburse you. US citizens should check with their insurer before leaving home to see what conditions are covered in their policy.
If you need immediate medical attention and you are in your hotel, your first call should be to the front desk. Some of the larger hotels have agreements with on-call doctors who can make house calls if necessary. In really urgent situations, you can call an ambulance (911), which will deliver you to a hospital emergency room.
If you can get to an emergency room, your best bet is the Tulane University Medical Center, located in the CBD.
Nonprescription medications and contraceptives can be purchased in the pharmacy section of drugstores such as Walgreens in the French Quarter. Other branches, and pharmacies such as CVS, are common around the city.