The answer depends on whether you are European and covered by European Health Insurance.EURPOPEAN
If you are European you should have applied for a EHIC (European Health Insurance Card) before you left and you will be covered by the Spanish National Health system
If you didn't get a EHIC then you can give them your passport number and then if you are lucky you can get someone to give you a backdated EHIC when you get home.
Look at this site for getting a EHIC http://www.e111.org.uk/
As you are in the Albayzin you might as well go to the Albayzin health centre.
(Centro de Salud Albayzín)
This is very near to Mirador de San Nicolas.
Behind the mirador is a big white church and then two terrace restaurants (the first is the Kiki),
The heath centre is in the corner behind the bars opposite the library (biblioteca)
They don't necesarilly speak English. Many of the doctors do but the reception staff don't.
The best thing to do is take someone with you who is bilingual.
If you have a mobile phone you could get someone to interpret for you by passing the phone back and forth.
If you are on holiday and have booked your accommodation with a bilingual agent then they would probably help you.
I know that granadainfo would definitely help you.
If your health problem is more urgent it is best to go to Traumatologia. This is the A and E department.
Avoid the Clinico because it is full of student doctors who don't have much experience. (This is based on my own experience and may be wrong)
As you are using the national health service you can't demand to see an English speaking doctor but almost all doctors speak some English because most of the literature about medicine is written in English and also theoretically all doctors should speak English.NON EURPOPEAN
Even if you have no insurance you could probably get treated in the same way as Eurpoeans although they will probably send you a massive bill.
If you have medical insurance phone up the insurance company and ask them to give you a list of the English speaking doctors available in Granada.Don't forget Chemists
Don't forget that chemists are very knowledgeable about medicine. If your condition is not urgent go to a "Farmacia" and ask their advice. This is much quicker that going to see a doctor. Private English Speaking Doctor
I have searched the internet and I can't find any private doctor in Granada advertising themselves as English speaking.
However, there is a German doctor in Almuñecar who speaks English.
Almuñecar is about 1 hour away by bus or car.
Here are the details.
Paseo del Altillo 4-3°C
Tel: 958 88 15 11