Could my asthma cause me to become depressed?

Yes, but: There is a strong association between depression and asthma. It's not clear which comes first but once present each exacerbates the other. For best result treat both asthma and depression.

Not directly...: The drugs for severe asthma (eg prednisone) can lead to depression, additionally, a lack of activity or severely restricted activity can lead to depression.

Yes, change it: Any inflammatory condition, especially if longstanding, can cause depression. Getting 30 -45 min of sunshine at noon daily or taking vitamin D3 10,000 IU/day and taking a good probiotic (not yogurt based) help reduce inflammation. Avoiding all milk products is very important since the milk protein causes respiratory tract inflammation. Yoga breathing exercises 10-20 min/day help too.