Baby with Asthma?

Amanda
My daughter is 6 months old and about a month ago started coughing weird while playing. We went to the doctor and explained it, it didn't sound like croup and she gave us an inhaler because several of our family members have asthma. I used it once on her and her coughing went away for awhile.
Last week it started again and that was around the time we started opening our windows. I thought maybe it could be our cats but she's had no physical reactions. Last night she was coughing bad so we used the inhaler and it went away immediately. This morning she started coughing again and I used it and she hasn't coughed since. 
Do any of you have babies with asthma or coughing problems? I feel bad for her 😕 she's happy though so that's good.