“Should I go to urgent care for sudden hearing loss?”

Sudden hearing loss could be a serious condition depending on the acuity, your age, or any other symptoms. If unsure get evaluated-

You should see an ENT physician and get a steroid injection through the ear and be referred for HBOT.

An urgent care would not have the resources to properly evaluate this issue. An emergency department would be more appropriate especially if there were other acute symptoms including headaches, dizziness or loss of balance, facial muscle weakness or facial pins/needles sensations (paresthesias). Hearing loss, alone, could start with an office primary care evaluation and audiology referral.