Any wheezing like this that is persistent should be checked out by a doctor
. You could start with your primary care doctor
who should be able to help you figure out what is going on.
The two most likely possibilities here are in fact asthma
and allergies, just like you have suggested. Asthma is a chronic condition in which the tubes inside the lungs periodically constrict or become inflamed, leading to cough, wheezing, and shortness of breath. There is a particular type of asthma, called exercise variant asthma, that is specifically triggered by physical exercise and might explain why your symptoms seem to appear primarily with exercise.
Nasal allergies can also cause some wheezing like noises. They do this primary by causing inflammation and congestion in the nose and dripping of mucus down the back of the throat. Other symptoms would include stuffy nose, sinus pressure, itchy throat, or frequent sneezing.
Your doctor will be able to examine your throat, nose, and lungs and help decide which of these possibilities is more likely. Based on what they find, they will be able to suggest an effective medication regimen to help control your symptoms and get you feeling better soon.