According to the Rules Reference, page 7:

• If an investigator takes damage or horror as a cost and reassigns any of it to an asset, the cost is still considered paid.

This rule therefore allows Painkillers to work alongside Peter Sylvestre, healing your investigator and putting the horror cost onto Peter to be healed off at the end of your turn. This combo allows typically low-health survivors to tank more effectively, and action-free once both cards are in play, although using up the supply doesn't discard Painkillers so it cannot just be spammed with Scavenging.

What is not immediately clear is just what can be healed. Since the card literally says "heal 1 damage" and doesn't specify from an investigator / ally / story asset / enemy / bulletproof vest, one interpretation is that any damage on any card in any location can be healed... expect errata soon. Or just Grim Rule it.