Contacting bittrex won't help because according to your statement, the coins are in coinbase so they're the only ones who can retrieve them for you.
Although I'm afraid you will have to wait for a few weeks or a month since this type of problem is not in their priority list:
Our team is prioritizing only trust and safety, account lockout, and delayed payment issues. Specifically:
Account compromises
Account lockouts (password resets, 2-factor authentication, device verification, lost access to email address)
Delayed payments or orders
We are unable to prioritize other issue types at this time.
If by any chance you didn't use a third party wallet like coinbase, You'll get your coins again in just a few minutes