Your concern is warranted. Your son may have asthma, but it is notoriously difficult to be certain about the diagnosis in infants. However the diagnosis can be established with reasonable certainty at his age of 3 1/2. The failure to demonstrate allergies does not rule out the diagnosis of asthma.
You have exhibited great faith in his doctors, but as you state, they "...don't know what to do." It is time to get this resolved. I strongly recommend that you request consultation with a board certified pediatric pulmonologist. You may have to take your son to a larger city to locate such a specialist but he must be diagnosed and treated effectively, if you or he are to get any relief. You could begin the search for the specialist by contacting the nearest children's hospital. If your son has asthma, there is effective treatment for it.
Good luck.
Hi. I'm sorry to hear about your little guy, but thought I'd let you know you're not alone. My daughter was not diagnosed with asthma until she was 5 years old. She was sick all the time, in and out of the doctor's office and ER, but still no diagnosis. She was given a nebulizer with 2 different medications, but they really didn't seem to help. Finally, I threw a fit, saying I was sick and tired of them not helping my daughter when there was clearly a very serious problem, and her family doctor sent her to an allergy specialist and an asthma doctor. She received an allergy test on her back, which revealed allergies to dust mites, and she was put on an inhaler. This inhaler has a spacer attached which is like a little plastic tube that the doctor says helps her get more medicine into her lungs. I also wonder if you or anyone else smokes in the home or the cars. We did, and stopped when we found out for sure she had asthma and she's done a complete 360. We were also referred to a visiting nurse type of program. A woman came to our home and showed us things that would cause problems for asthmatics. (Stuffed animals carry dust mites, not to vacuum carpets before bed because it stirs up dust, she needed a special pillowcase and mattress cover, among other things we never would have thought could hurt her.) If you have any other questions or whatever, just let me know and I'll try to give you our experiences with asthma.