If you are sure that over the next 15 years you will be able provide a good life for your cat, then it is a wonderful idea. During the first couple of months, kittens are especially playful and fun to be around (while not being loud!).
Tinnitus Talk Support Forum
In a couple of months hopefully your tinnitus will begin fading and you will begin to feel better. So it would seem to me that adopting a kitten would provide you with a positive distraction that you need at this difficult time.
Do you want to devote hours a day on playing with your cat? are you ready for those times where you get annoyed cause it's getting into naughty behaviour? Are you ready to get woken up early, or in the middle of the night sometimes? If you can say yes to all of those, then I think it's a wonderful idea.
I got a kitten some months after getting T but I found I was not ready for all those things, I mentioned before, so I gave her a new home as I couldnt provide her with the attention and love she required.
Cats do wake up their owners, but I think that if you live in a house, if it is important for you to not be woken up, you can avoid it. Close the door of your bedroom, and close some other door to prevent the cat from being and scratching on the other side of the door to your bedroom. Problem solved.
Yes. Is good idea 
Here is how to train your cat to let you sleep:
https://www.youtube.com/watch?v=umngBzK0j2Q
https://www.youtube.com/watch?v=umngBzK0j2Q
There are some benefits to adopting an older cat:
https://www.youtube.com/watch?v=9JcB5fLAKbk
https://www.youtube.com/watch?v=9JcB5fLAKbk
I adopted two kittens last year for the sole purpose of getting my mind off t, and I'm a cat person.