How painkiller pill would know where the pain in the body??

In fact they wouldn't!!..then do they act blindly??
Actually damaged body cells produces a large amount of enzyme 'cyclooxygenase', which acts on cell membrane and leads to the formation of prostaglandins(hormone like substances), which in turn send pain signals to the brain; additionally swelling, redness are also mediated by them -- Pain

Painkiller Pill -- aspirin like drugs when taken, enters into the blood stream, travels all over the body and where the level of the enzyme cyclooxygenase is high, it binds to it and prevents its functions;
So No prostaglandins produces > No pain > No pain signal to nerves system.

         But pain isn’t always bad, even if it doesn’t feel very good. Pain is our body’s way of warning of something is wrong so we could fix it. If we didn’t feel pain, we might not realize that there was a problem, and it could get much worse before we notice it.

...and little about painkillers.. broadly they are of 2 types:
type 1 - they don’t remove the pain. Instead they act on the pathway which sends pain signals to the brain and also in the brain to alter the perception of the pain;Steroidal
type 2- actually removes the pain itself; which we take over the counter/ medical shop; Non Steroidal

disclaimer - terms/ biological short answers used may not be 100%, roughly 20 mins of googled knowledge, hence limited understanding.

PS: may be should stick to type 1, do you?