Can meds that are expected to make you drowsy cause insomnia?

Once again I am baffled by the effects of taking a medication that I thought and expected would make me drowsy. I’m taking it for pain, not for sleep (I normally have no difficulty getting to sleep), and taking it at night, so being drowsy is fine. Lying awake for one to three hours after taking it is not fine. I’m in a bind because I can’t sleep with the pain either.

This particular medication is Tylenol 3. I’ve looked up the side effects, and insomnia is not one of them. But this is the only change in my routine, and I am normally a somniac.

Question: Is there a way to tell whether a particular medication contains an ingredient that is supposed to offset drowsiness? I remember experiencing this effect before, with cough medicine containing codeine, and lying awake half the night with it.