With the right medication you should be able to function normally with asthma, the only issue (i'm guessing) would be if you wanted to compete professionally as at least some of the medication used to help with asthma will be on the banned substances list however there have been a number of professional sportsmen and women who have had asthma and have gone on to compete at the top of their chosen sports. It's worth pointing out that the genetic links between parents and children in regards to asthma are generally focused at childhood asthma rather than onset adult asthma and it is not a single "asthma" gene that means you will get it, think of it more that some people have a genetic disposition towards asthma, in other words they are more likely to develop asthma as a side effect of something like a respiratory illness or irritants. There is no way to predict your chance of getting asthma but i would say with absolute certainty that just because your father developed it does not mean that you are going to and i would not spend any time worrying about it as even if you do get it once your medication is sorted out like OU student said you will be able to continue your training with minimal if any interuptions.