No. Most cases of ringing in the ears (tinnitus) is not due to allergies. It is a common condition in older folks. It is usually caused by nerve damage (of the nerve that carries sound). It could be age related, hereditary, or form damage from constant exposure to loud noises (gun fire in the military, loud rock music etc.,) or rarely after some antibiotic use and eustachian tube dysfunction.
Tinnitus. Possibly, but no probably. Tinnitus is usually a sign of hearing loss. But sometimes it occurs with allergies causing the ears to be blocked.