Do allergies cause eye strain?

Generally not. Muscles inside the eyes contract when near work (like reading) is being performed. Prolonged periods of such contraction can lead to eye strain and headaches; glasses can support the muscles so they don't have to work as hard. While allergies can affect the tear film and have an (usually temporary) impact on vision, they generally do not cause eye strain.
Allergies. Sometimes. Allergy and allergy meds cause the eyes to become swollen and irritated. Medicine that dries the sinuses may dry the eyes and make them feel tired, gritty, or strained. In this case, try using some artificial tears such as systane.