The short answer to this question is, 'maybe.'
HEPA air filters work by reducing the circulating particles in the air. Many people with asthma
to have allergic reactions to particles that worsen their asthma symptoms (types of particles that can do this include mold, dust mites, pet
dander, cigarette smoke). Thereby, in principle reducing the number of these particles in the air can be helpful.
However, filtering the air is not a definitive treatment. In particular it is not a substitute for eliminating source of the particles. For example, if the problem is wall to wall carpeting, the solution is not a HEPA filter but rather taking out the carpet. Similarly, if the problem are smoke vapors, the solution is stopping smoking, not using an air filter.
Similarly, for most people, asthma cannot be controlled solely by eliminating the sources of the inflammation or filtering the air (although this can be important). It is almost always necessary to also use a controller medication, like an inhaled steroid.
If you feel like your asthma is not well controlled then the first step would be to go see your primary care doctor
or your asthma doctor and talk about your symptoms so that you can come up with a plan for feeling better.