Is it possible to have asthma diagnosed even when you're not in the midst of having bad breathing difficulty?

I'm 47, and no one in my family's ever been affected by respiratory illness, so it's something I've never thought about. A little over two months ago, I began having some symptoms that at the time I thought were related to a new medication. I was getting very winded with very little exertion, and I began to notice a strange sound almost like snoring, but more raspy when I would get tired. Also, when lying down, my breathing would sound weird at times. Then, I got a cough, not frequent, but bad enough for people to comment on it. Now, I feel at times like I can't breathe deeply. I'm really tired. My son was sick last months with chest pain, an uncontrollable cough, and what they determined in the ER to be a viral bronchitis when it seemed to be getting no better after two weeks. I'm now 99%sure that we have toxic mold in our home, which I'm tending to ASAP, and very worried about the effect it's had on my family. I want to get tested for asthma, but at this moment I don't feel very bad.