(StopAN1 - love the name. After my surgery my password was similar G3tThisAN! for a while)
I had CK, about 6 months after surgery. In the surgery they removed both the hearing and balance, so my story is a bit different.
BUT - i travel a LOT for work. A lot. This year I have been to Japan, Poland and India already.
The very first flight i took i had horrible headaches, and really struggled with resting. Its a bit better now, as long as i make sure I am rested and stress free. No new issues with balance (my new normal is that balance is a challenge, due to the surgery) when traveling. The tinnitus is super loud on the planes, and I use noise canceling headphones all the time.
Hope you both do well!