B.D.
My daughter is older but suffers from really bad allergies. The pediatrician did blood test and they were negative as well. When I spoke to the allergist he said that is is very common for the blood to show negative until they are older because the IGE attach to to the mast cells...
Every 2-3 weeks sounds more like there is an allergic trigger. It sounds like you need to take him to an alelrgist and have the skin test. Those results would be more definitive as to what he is allergic to.
My allergist also says that asthma is not a disease but a symptom. If you find out what he is allergic to and get the allergies under control, his asthmatic reaction will probably dissipate as well.
Claritin is approved for children 2 and up. We have found Benadryl to be far superior but you'll have to see how he reacts with it. Some it sedates, others it makes hyper, and then some are just fine with it.
Hope this helps!