Could my asthma be triggered by exercise and allergies?

Yes. About 60% of asthma is "allergic asthma." this is asthma that can be aggravated by environmental allergies (e.g. Dust mite or cat dander or ragweed). About 40% of asthma is "non-allergic." common triggers of non-allergic asthma include exercise, cold air, respiratory infections, or emotion.
Yes... Both allergies and exercise are common asthma triggers. Try to avoid allergic triggers and a bronchodilator inhaler can be used before exercise to avoid exercise-induced symptoms.