As you noted, the pain medication doesn't kick in very quickly after you push the button. Maybe it would be nice to make a distinctive sound when medicine is being administered, and a different sound when the button is pressed during the delay period or after the lockout. There is a substantial placebo effect in pain control. So maybe the pump should always beep the same, whether you receive pain medicine or not. The primary problem here, however, is the doctors.
Doctors are inappropriately concerned about addicting patients to narcotics.
When they do cause addiction, it is in patients with a history of prior addiction, especially to drugs, alcohol, or cigarettes. I did leave out the base rate medication, but purely for the sake of simplification. The stupid pump I had also beeped, but I considered that fairly unimportant since it didn't indicate anything beyond the button having been pressed. A beep that occurs regardless of whether the action has been successfully communicated is less than useless. Such a beep is about equivalent to those silly seatbell warning sirens that fire off regardless of whether you have put on your seatbelt.