No, you don't need to re-size again, you can tumble it for a week it's still the same dimensions you sized it to.
If you full-length sized, next reload consider neck-sizing only, presuming you are working with rifle shells.
You can skip the walnut cleaning and go directly to SS pins. Or vice versa. I prefer SS pins since the walnut media is dusty and the tumblers noisy. Your choice, you can't clean your brass too much.
Do not resize dirty brass, you'll wreck your die. I know a reloader who cleans his brass before initial inspection, again after inspection/depriming, again before sizing/reloading. I think he'd clean it again if he could add another step to the process. It doesn't hurt the brass and does make handling and inspection a lot easier.
During your SS pin cleaning period, if you change out most of the water around mid-cycle you really get good-looking brass.