I had a similarly frustrating experience initially that was resolved extremely professionally by Etihad.
Similar situation, AA ticket number, EY flight number, booked through TA. Tried online, didn't receive confirmation. Called Etihad, they said I would need to speak to AA. Called AA, they said the TA would have to do it. TA tried it, came back unconfirmed as well.
Called EY and told them I was tired of calling people, and an excellent customer service rep took action and fixed it by asking the service provider to manually force through the booking, and sent me a confirmation email a few hours later.