Which is more important? Not giving your child medications or you child being able to breath? Have him evaluated by an allergist and have PFT's (Pulmonary Function Tests) done to see if he truly has asthma. Claritin will help with the allergy but will do nothing for asthma! If your son's airways are inflammed only certain types of medications will reduce that inflammation.
In a pinch caffine can help because it dialate the blood vessels and more blood means more O2...but less sleep!
If your son says he is having trouble breathing and your family has a history of asthma TAKE HIM TO THE DOCTOR! Many with mild asthma will have their symptoms at night, coughing, even in their sleep.
There are many things that can reduce the frequency of flare ups. If he is allergic to dust, wrap ALL the pillows and mattresses in the house. Get rid of carpeting (especially in his bedroom), have you air ducts cleaned if you are in an older home.
I have two sons with asthma. My youngest has been hospitalized twice with it! Once your asthma gets out of control it is a very quick spiral down. Even though we were doing everything we should have (my husband is an MD, I am a former EMT) the last time when we got to the ER his Oxygen saturation was 70%!
Think of all the needles and treatments that your son would have to go through if his asthma remains untreated and gets out of control. Is a daily preventative inhaler or pill worth it? I would hope so. I don't mean to be harsh but after working in an ER and dealing with a parent whose child just died because of their asthma being untreated (in that case the family couldn't afford the medicine) sticks with you.
Sometimes we have to go against what we really want and do what is right for our children. Good luck!