My eyes are constantly burning. Could this be due to allergies?

Possibly. The feeling of burning of the eye surface is common and actually most often due to eye dryness. If accompanied by redness and clear discharge, it might be allergic. If the vision is preserved and there is no pain, then you can try over the counter lubricating eyedrops for the dryness and anti-allergic drops for the possible allergy. If persistent, see your ophthalmologist.
Unlikely. Allergies tend to cause itching and watering. Dry eyes and blepharitis often cause burning. Try some artificial tears and see if this brings relief. If it does, it's probably dry eyes.