Oh Rid, I feel for you. I too was allergic to dogs as a child and remember the day when the tests came back to say I had finally outgrown the allergy. I was sooo happy I could finally get a dog.
It's obviously worse with you having asthma too.
Obviously don't let the dog sleep on your bed and make sure you hoover and clean more than what a "normal" person would do. Ensure you have an anti allergen hoover with the right filter and then hoover at least once a day. Get rid of all the stray hairs.
When you're allergic to an animal it's the saliva you're allergic to. So when a dog or cat licks themselves and then you stroke them, you get a reaction. That's why a lot more people are allergic to cats as cats are big on grooming.
So try not to let your dog lick you.
As you shouldn't bathe your dog on regular basis as it's not good for the fur coat, get yourself some pet wipes so you can wipe your dog down more often.
I did read in a magazine that apparently there is a dog shampoo that helps for when people are allergic. It was in the K9 magazine.
If all else fails then you could see your GP for an antihistamine injection. Depending on the relationship you have with your GP and whether he/she is an animal lover, I might not say you want it because you're allergic to your dog as he/she might say you should get rid. As you already have asthma, explain that you think you may some other allergies too. You could say you have hayfever and then when the injection wears off (I think it last a good few months) you could go back and say something is still triggering a reaction just don't mention you have pets.
Hope any of above helps