I am allergic to dogs, and they do make my asthma worse. Because I had always grown up with dogs, I never really noticed it until I went to college, and I would come home to visit. For the first couple of days, it would be really bad, especially if I let him lick me. If I slept with him, I almost always woke up wheezing really bad and would have to use my inhaler or machine. After the first couple of days, it would calm down, though.
Frequent baths and using all natural shampoos will definitely help, but if you're also allergic to the saliva, you'll probably still have some problems. As long as I'm able to keep it under control, it's worth it to me, though. Hee, it's like my allergist said when I was young, "I see we have a dog and we have an allergy, and I suspect we're going to keep them both."
I'm also very allergic to cats (more allergic to them than I am to dogs), but it doesn't ever calm down, no matter how long I'm around them. Funny thing is, I was never allergic to cats until we got one, when I was around 12. Then, I developed.