Do you think she has asthma?

All kids sweat when running around playing. It sounds like she just has a bad cold/infection. Doesn't sound like asthma. Wheezing is the main symptom. If she's running around and playing and doesn't wheeze or seem tired all the time after running, she probably doesn't have it. Believe me, you'd know if she did. But, watch her closely with this infection--it can turn into pneumonia or RSV very quickly. Additionally, some viruses have been known to cause asthma after the illness has ped, so keep an eye on things. Make sure she's well hydrated--that will help a ton.