Does amoxicillin make the infection in your tooth release a dishcharge in your mouth?

No : No it is a broad spectrum antibiotic effective against most gram positive bacteria in the head and neck area of the body. It will reduce and kill the bugs causing a tooth infection usually an abscess under the bone and gum tissue.

Antibiotics: The drainage you are tasting is puss and you should spit out if you taste it. The antibiotic will help get rid of the infection and the drainage, but only for short time. It'll be important that you get definitive treatment to eliminate the cause of the infection.

Draining infection: While Amoxicillin is often the most useful antibiotic to help control the spread of oral infections, it alone cannot eradicate an infection, especially an acute one that is draining pus. It also requires removal of the cause of the infection with definitive treatment and the body's own defense mechanisms. I hope that you are under the care of a dentist for this infection.