You should for 3 to 5 days. If there is no more cheese or swelling he'll probably be ok.

Be sure to be aggressive in your cleaning. Give a squeeze above the infected area, like you would a needing-to-be-popped pimple, to be sure you're getting all the gunk out. If you don't an infection could set in. It sounds worse than it actually is. Just clean it out good and you should be ok.