are painkillers and other medicines a form of alchemy?

Depends on your definition of alchemy.

My impression is that back in the day most alchemists focused on metals and on compounds that burned and released energy impressively, so no, that didn't lead to modern pharmaceuticals.

On the other hand, herbology, the study of plants that seemed helpful to sick people did contribute somewhat to modern medicine as scientists studied why and how certain herbs helped.

No, but with the pain I was suffering a month ago, painkillers were all that kept me sane.

No.
But a lot of them are not as effective, or as necessary, as the advertisers would have you believe.

If you want to get technical, chemistry is at least partly based in alchemy. The pharmaceutical studies are based in both chemistry and herbalism, so you have alchemy and witchcraft in their history.