Staph infection how much of an emergency is it?

Buddy has staph infection, Getting yellow, pusy, more swelling around site. Skin around almost a greyish? How much of an emergency is it? Is it ok to wait until tomorrow?

Nobody can answer that. There are over 30 different kinds of staph infections, some more dangerous than others and some will kill you. It is always a case of the sooner it is treated, the less of a problem it becomes.