Is respiratory allergy one of the many reasons that can cause mild chest discomfort? is it only in rare cases?

Chest pain: Yes and it is not rare to occur. Best to see an allergist to determine the cause and to help you prevent complications e.g. Asthma.

Probably: If by respiratory allergy you mean asthma. In asthma inflammatory narrowing of the breathing tubes makes it harder to empty the lungs of air. At the end of exhaling there is more air left in your chest than normal. This is called air trapping. Trying to exhale against resistance is tiring and results in discomfort. In asthma it's your chest wall not your lungs that hurt.