We have cats and a cat allergy in the family and here is what we've done that has helped a LOT!
1. Definitely do the Allerpet. The best way to apply it is to use one of those painting sponges on a stick. Put some Allerpet on the sponge and apply it opposite to the way the hair grows so it goes under the hair and on his skin where the dander is. Apply it generously on the dog's genitals where it may lick a lot. We have to use Allerpet several times a week, not just once. I alternate between Allerpet and special wipes that get rid of allergens. I wipe the cats down every day.
2. Invest in a good air cleaner for your son's room. I suggest the Honeywell brand because their HEPA filters last quite a long time. Vacuum off the filter once a week. Run the air cleaner on low all the time, and move it to high if you remember during the day. We got a big air cleaner for the family room too.
3. Invest in an anti-allergen detergent and wash your son's clothing in it.
4. Is he allergic to dust mites? It's a common allergy. Putting a dust mite cover on his mattress and pillows can help a lot. Also, wash his sheets and blankets on HOT or get DeMite laundry additive. He could have too many allergens overrunning his system and getting rid of some may help.
5. You can buy a spray that kills allergens on fabric. Use it on the places your dog likes to frequent. We use it on the couch once a week.
6. Invest in a steam cleaner. I got one on amazon.com for $80 and I love it! It's a Wagner. I use it to steam clean the floors, I also steam clean the couch and once a month I do the carpet.
7. I wipe down the walls once a month with a damp rag. Dander sticks to everything.
8. I vacuum daily. You may need to experiment to see how often you need to vacuum. Make sure you have a vacuum with a HEPA filter and a HEPA vacuum bag or you'll just be spraying the dander back into the air.
I know it sounds like a lot, but I could NOT part with my cats! I had to find a solution and I did! The work is actually not that much now that I have it down to a science. We live in a small apartment so it takes me maybe 10 minutes to vacuum, 2 minutes to wipe down the cats and maybe 3 minutes to vacuum the couch and spray it down. 15 minutes a day is definitely worth it to me to keep my cats AND my allergenic husband!
Good luck!