So that may be your ticket after all, I don't really know. Anyway, for now it doesn't matter having a ticket number or not. What matters is that you received that automated message. I know it doesn't answer the why, when and what will be the outcome, but it means that support did receive your message and now it's placed on the queue awaiting for review.
When Chaturbate issues a ban, no matter if it is manual or automated, they never send messages, emails or any kind of notification to the user. It is expected that you know of the ban when you try to login into your account and then contact support if you decide to appeal. You said you noticed the ban and contacted support a week ago, so that's when you 'opened your case' and began your wait for their answer. One week is well within support's time to respond, so try to be patient. In my case, on two different occasions that I had to contact support, their answer came after 9 and 10 days. Of course every case is different and depending on what they have to do in order to review your situation and their workload it can take less, like a couple of days, or more, up to a few weeks.
Wish you luck.
