There is no known connection between BP and fainting. Migraines and BP, yes. I have lived with the illness since childhood (41 now) and started fainting in my early teens, there are many causes of course, but mine was attributed to hypoglycemia (low blood sugar). Sugar is glucose, one of the body's electrolytes. This can occur in people sensitive to sugar in the form of sweets or cakes and breads (pizza included). It can happen 3 or so hours after ingesting these kinds of foods because once the blood sugar spkes, it dips down and can cause fainting. (Syncope). Also, it can happen when a person HASN'T eaten. Anorexia and bulemia can also be the culprit. Many BP women have eating disorders and are very secretive about them; of course many teens WITHOUT BP have eating disorders. Look for any type of clues. Eating a lot at one time may mean purging afterward (throwing up). Or of course, eating tiny amounts or not at all. Overly exercising can cause it too with too little energy from food. IMPORTANT: people with eating disorders are not necessarily too thin; esp. bulemics.
EKG is definitely in order, just to rule out any kind of heart abnormality. Eating disorders can upset electrolytes which are the 5 chemicals that keep the body working properly and if they are off for too long or to severely, it can kill and definitley cause fainting. Eating disorders almost always do this, that's what causes the deaths.
Abuse of laxitives and water pills also can upset electrolytes and again are hallmark signs of electrolyte imbalance due to eating disorders. Drininking way too much water (over 4 litres a day) can decrease sodium in the blood which is very dangerous, low potassium from diuretic use can affect the heart adversely as well.
She desperately needs to see a doctor for a full physical, blood workup, EKG, EEG (brain test), CT of head and chest, chest x-ray and whatever else her doctor may decide, preferably an Internal Medicine MD, whose specialty is diagnosing illnesses rather than a pediatrician.
These are the most common things that could be causing her fainting; a 15 yo DEFINITELY should not be having these episodes.