Does this sound like asthma? Please help?

Well, it all started last year when I had to run the pacer during PE. In case you don't know, it's this test where you run back and forth across the gym and you slowly increase in speed. I really pushed myself and got a 75% (around 30 times across the gym). I had to stop running because I felt like I was gonna p out. It made me feel horrible. It was near the end of the day and as soon as I got in the car to go home I started crying.....and I'm not the type of person who would do that. Then i was really pale and felt weak and horrible all night after running the pacer and I stayed home from school the next day. I have gone to the doctor since then and gotten an inhaler and a note saying I can stop running, but the doctors still don't know for sure if it's asthma. My gym teacher seems to be understanding, and doesn't penalize me when I fail as long as I try. Today I could only get 11 on the pacer because I started feeling out of breath and i knew if I ran much more I would make myself sick again so I stopped and my gym teacher told me I could stop whenever I wanted before cl. And for a while after i ran 11 times for the pacer test, I was talking to my friend and I felt kind of out of breath and my voice was slightly hoarse....like I had a frog in my throat or something but I didn't. And after I run it seems like my heart rate stays up and my heart keeps pounding for a while after.....is that normal? Basically, I start running and at first I breathe in through my nose and out through my mouth. But after 30 seconds to a minute or so, I start feeling bad and I have to breathe through my mouth because I feel out of breath. I even get a little out of breath walking fast through the hallway with my heavy backpack. I don't feel like I'm breathing through a straw, just out of breath. And I'm not overweight or anything......and the inhaler helps, but I still have trouble. Does this sound like asthma? If not, what else could it be? Thanks so much :) Oh, and I do use my inhaler before PE which helped last year. I have gone to a pulmonologist and was prescribed a different inhaler that I use every morning along with my other inhaler that I use before PE. They did a couple tests on me like the peak flow meter, and they said I had excellent lungs, but that I could still have asthma.