How often can I take Advil if my eardrum hurts, when I take Lyrica (pregabalin) 74mg, hydricodone 10-325 and Etolodac 500mg twice a day?

Not at all. You are already taking another anti inflammatory medication.
Stop. You are taking way too many drugs, all those meds just mask the pain, not treating it. Find a good ENT to treat ur problem and stop taking narcotics for ear pain.
NSAIDS. Since you're taking etolodac, taking advil (ibuprofen) would be redundant as they are both nsaids. Have an ear exam and perhaps antibiotics and ear drops would help you.