Does allergy and asthma go hand in hand? My son has being diagnosed with allergy, but nothing is helping and we do have a large dog so I wonder?

Yes. Allergy and asthma often go hand in hand. Have your son see an allergist to be tested to see what he is allergic to specifically. It may or may not be the dog. Foods can also trigger problems.
Yes. Approximately 80% of children with asthma have an allergic trigger. In adults it is estimated that about 50% of asthmatics have an allergic trigger. In children they go "hand in hand" so it is paramount to address allergic triggers in children with asthma especially if it is not controlled. An allergist can determine if dog or other allergies (or non-allergic triggers) are contributing.