As one with asthma and horrible cat allergies, I can relate.
I know you love your cats, but your child has been suffering for a year. You just took him to the ER. Asthma kills, especially young children whose respiratory systems are not fully developed.
GOOD QUALITY, large hepa filters all over - in every room. Why not just in the child's room? Because you all get hair/dander on your clothes and carry it all over the house.
Remove all carpeting. This will help your child immensely, whether you keep the cats or not.
Get a vacuum with the best possible filter and vacuum often.
If you have cloth covered furniture, vacuum it a lot. Leather is so much better.
Ventalin is great for treating asthma attacks. All medications have an effect on the body - if nothing else then at least on the livers/kidneys that have to filter. To me, they are the last resort, not the first.
Please do your best for teh child, as I am sure you will.
Good luck to you, and I hope you find a way to keep your kitties