I'm not sure what you're saying starting with ",des say........Who says it's asthma? Why doesn't he have meds for asthma? Or are you saying meds don't help? What are the meds? What treatments have you tried? You say allergy meds don't help? There are many different ones. Which ones have you tried? Without knowing what you've tried I can't suggest different ones to try.
My granddaughter has asthma. She has had to try different meds until she found ones that worked for her. And allergies worsen the asthma. I suggest allergy testing. Then avoid what he's allergic to. For example, when my daughter was younger she couldn't play outside when the trees were in bloom.
One thing that could help is to use a humidifier in his room at night. AZ air is quite dry. Perhaps a whole house humidifier would help.
If it's post nasal drip a neti pot might help. It's a way to wash out the sinuses.
Have you tried a prescription cough medicine with codeine?