Flu can make you generally feel ill and very tired and out of breath when you push your body too far. However, respiratory infections are a major asthma flare and many people have infections that trigger the asthma to start.
I would keep a close eye on your symptoms and how you feel. If you get severly out of breath, get someone to take you to the doctor ASAP, since it could be a major asthma attack or the start of pneumonia, both which need immediate treatment.
If your shortness of breath does not bother you at rest and improves as you start to get over the flu, I wouldn't worry too much but watch to see if the symptoms ever get worse again.
I would skip gym class for a bit until you feel better anyway, it is a big stress on your body to be running around which it is trying to heal you. Ask your gym teacher for a pass unitl you feel better. Get a lot of sleep, fresh vegetables and juice (or juice if you can't eat the fruits themselves without feeling worse) and relax and let your body heal.
Hope you feel better soon.
Possibly. Have your mother take you to the pediatrician.