Well, being a chronic asthma sufferer for more than 2 decades, I know that you can't 'catch' asthma.
The following link has info on asthma, including saying that most people that have asthma usually have a family member that has asthma, eczema, or a combination of both.
http://www.medinfo.co.uk/conditions/asthma.html
I suspect that something you have worn or slept on in the past few days has given you some sort of broncial alergic reaction, not full blown asthma.