How can I stop a pilonidal cyst from draining pus, my boyfriend has seen a doctor and they said their is nothing he can do yet since it just started?

Incise and drain. A general surgeon or colo-rectal surgeon might be able to clean it out with minor office surgery or excise the cyst in the or but you want to control the infection and draining is good to allow the cyst to calm down.
Impossible wishes. First why would you think that you can change what nature does in this kind of infection. He must drain the pus to get rid of it. Never would you want to interfere with the natural healing process of an infection.