It can restore maximum Health lost through the usage of Telltale Hearts and Florid Posterns. It will not increase one's maximum Health past the default.
The item restores missing maximum health, without modifying actual health.
Always adds 25% of the base character's health value to the current maximum health value, except if this latter is already at its base value, resulting no change.
The booster shot is used for medicine to upgrade the body's immune system to fight a virus that may come later in life if not given the booster shot. However, in Don't Starve Together, the booster shot is used after the character has been affected by maximum health penalties.
Having Rot as an ingredient refers to Penicillin, an anti-biotic derived from mold.
Bugs
The Booster Shot can be used on a Shadow Creature. The item will be consumed and results in no effects whatsoever.