You may exhibit on another day at another show only if it is an event with a seperate show number. You also have to consider if you have socialized, dined etc. with the panel of judges if it would seem "appropriate", even if the specific rules do not address it. Use good sense and do the "proper" thing to avoid tongue wagging.
You certainly can show the next day. Especially since it is a different breed. That said,it is always best to not give even the appearance of impropriety.
Once you start judging no matter what you do there will be some tongue wagging. It's some show people's second hobby. What they will say is that as a member of the judging panel you were in contact with the judges "last night" and now you are showing under one of them. It is truly a no-win situation. The only way to avoid it is to not show at all at that circuit.