Can a child grow a tolerance or resistance to allergy medications?

Tachyphalaxis. The tendency of meds to become less powerful after use is common to some pain meds but not allergy meds. More often, parents or patients get frustrated when congestion remains and blame the allergy med. However, allergy meds will never help irritant swelling or drainage caused by the simple irritant effect of air pollutants like smoke,dust, fumes etc. Other meds are available, but must be added.
Unlikely. Although you may consider rotating your daily allergy med among several subgroups availiable.