However, if you are less than 8 yo and you have not received flu shot before, then you need to get two shots one month apart the first year. After that, only one shot is needed per year. There is concern about slowing growth with this medication. However, a recent study showed that even when growth slows down in the first year of use, it usually catches up. The second part of your question is will your son outgrow his asthma.
Many kids wheeze in the first six years of life.
Some asthmatics are very sensitive to weather changes. You can test this by doing regular peak flows and seeing if they decrease during weather changes. Otherwise, you may need to take more than one pre-treatment medication. Most exercise-induced asthma is easily treated. Talk to your doctor.