I have asthma and lately even with my medication, I feel very short of breath. Is there any way to increase lung capacity?

Asthma. It might be something more than just your asthma or it might simply be an asthma exacerbation as it is viral season. I would definitely see your asthma specialist as you might simply need a more thorough controller therapy asthma action plan.
Depends on why. It depends on why you are ill; uncontrolled reflux, vocal chord dysfunction, uncontrolled post nasal drip, allergies that are untreated, may all mimic asthma (and don't respond to standard asthma treatment) or make asthma worse. See your pulmonologist or allergist and let them know what is happening.