What is the most logical next event?

How to get unbanned from omegle
Consider waiting a few days.
Omegle bans typically don't last longer than a week, so if you can wait your ban will likely go away on its own. If you can't wait, you can try getting a new public ip address.
Open a google search and type " my ip " to find your current public ip address. This is the address that omegle sees when you connect, and is the address that they used to ban you.