If some of it is asthma, then by definition that is reversible, and you should be able to get some improvement. I am a huge fan of
Singulair (montelukast), which can treat the allergic reaction in both asthma and in allergic rhinitis. I can't practice medicine here, but you could ask your PCP for a trial. It begins working within a few days. I don't know of any contraindications to it, except allergy to it.
It's approved down to age 2.