Go to google.com/history and clear out all history from all services. Go to YouTube and do the same. Clear everything from your browsers, meaning you have to log in again. If it's allowed, return the phone to its default state.
Just for good measure, power the phone off, take the battery out, wait an hour, put the battery back in, and power back up again (this part is cargo-cult, I know).
There are probably even more sanitary measures I'm missing here.