Prior Authorization but being billed? Possible appeal

Hello! In August I had a surgical procedure that was medically necessary, and I received a prior authorization for it (which I have the number for, thank goodness) I was told it would be covered and I’d owe $350 for it.

Now, I am getting a bill from the hospital I had the procedure at for $11k. Immediately I called insurance, they said they’d have the hospital rebill it to them, give them a month and call back. I called the hospital to let them know I wasn’t paying on it while it was in dispute. I called insurance a few days ago and find out nothing is being rebilled. Every person I get with the insurance company immediately tells me it’s not covered, that’s why I have to pay it, until I give them my authorization ID # and then they say they’re looking into it. I was supposed to be getting a call back from insurance but never did. I have been getting call reference numbers and everything. I am not very knowledgeable with insurance and I am afraid I have a time frame to handle this. I don’t plan on staying with them for next year and I’m worried if I’ll have to deal with this still, how long they’ll keep my information on file if I’m no longer a member. Does it sound like I have to appeal it, and how do I do that? Or is there a way they can fix it so I don’t have to?