Both my easy child daughter and difficult child son went poopie in the tub and refused to take baths for a cpl wks. It was aggravating but funny at the same time.
They got over it. (I think I moved them to another bathroom... they didn't seem to "get it" that it was their behavior and not some creature from the black lagoon, LOL.)
Does your son have a fever?
The fact that he's drinking a ton means he's not really on a hunger strike, or at least, is only on one to the limits of his 3-yr-old capacity. He's not going to starve if he's eating at school. My kids have done that and we just put food in front of them, ate dinner as usual, and cleared their plates when we were finished. Eventually, they forgot why they'd quit eating and they started eating again.
When he starts eating again, don't spazz out! Act normal or he'll realize he can manipulate you.
My husband has asthma and when he wheezed badly, he felt like he was drowning, and he quit eating. His parents were so alarmed, that he realized it was a great manipulation tool. So he quit eating any time he wanted something (usually attention). So if your son is truly sick, you still don't want to make a big deal out of it or he'll learn that this is one of your triggers.