Daughter ran mile, had blood like taste in throat & mouth dizziness, trouble breathing. Drank water still had taste of blood no blood visible. Asthma?

Asthma unlikely. You have a 9!year old daughter. She ran 1 mile. She tasted blood, was dizzy and had trouble breathing. It is unlikely to be a true asthma. She most likely improved with rest. See your pediatrician. A physician supervised exercise regimen is important. Pulmonary hypertension is rare and that is part of your question. For future sports it is worth the visit.
Trouble breathing. This symptom by itself warrants an urgent trip to the nearest emergency room now.
Needs to see doctor. Dizziness and trouble breathing while exercising can be sign of asthma, lung problems or related to the heart and deficnitely needs to be checked. Tasting blood could be because there is local trauma in the throat or mouth or sometimes could be related to lungs. Please take her to a physician to be checked as soon as possible.