If you have allergic asthma, you need to be careful not to take any alternative/natural therapies without talking to your doctor. Some of these have hidden ingredients that may set you off or may be derived from something like ragweed.
You are not really on a lot of meds (unless you are taking some that you did not mention), and if you are really only on inhalers they do not impact the immune system nearly as badly as oral prednisone, for example. If you are not taking a multivitamin, that would be a good start. As always, ask your doctor.