Exclusively English-speaking ambulances are non-existent in Barcelona. If you are in an emergency medical situation, call 112, the national emergency number. This is staffed by multilingual operators who will most likely be able to speak English. The fact that you are an English-speaker will be noted when your call is answered. However, it is always helpful to have a few Spanish phrases handy in case of emergency, or, be able to call upon a neighbor or friend that might be able to aid you with the call.
When you arrive at the hospital, you should be (or request to be) assigned to an English-speaking doctor, or, someone on staff that can act as a translator and help you out.