[*Shira*]

One of my friends who does have asthma survived Cairo by taking with her a supply of the disposable masks that people wear over their noses and mouths to protect against germs. She wore them nearly all the time. In order to avoid attracting attention with them, she took a long rectangular scarf and wrapped it around her face in such a way that only her eyes showed, thereby covering the mask. Because she covered her hair and wore loose-fitting long dresses, people just assumed her to be a conservative Muslima and therefore she didn't draw any strange reactions.

So, the above solution would probably attract the wrong kind of attention here in the U.S., but in Cairo it would probably just cause the locals to treat you with an extra level of respect!