I also have asthma and have the tingling arm (occasionally leg) on my left side. It comes and goes and I cannot figure out what triggers it. I was prescribed Ketoprofin but it doesn't seem to help. I don't know if you are on any sort of inhaler for your asthma but when I take my Ventolin/Albuterol, it does help the tingling go away.
I even went the ER for it two months ago and they said it was my asthma as well. Hope that eases your mind a little.