Broadly speaking, to "be on a pill" would mean to be under the "influence" (for lack of a better word) of a pill. For example if a woman is on the (birth control) pill, it means she's taking such pills in order not to get pregnant. Similarly, if someone is "on" drugs, he or she is under the influence of those drugs.
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arman19940326 The pill that I’m on is a tough one to swallow."I'm on" here means somehow "I have to swallow"?In a way. It means that you have been prescribed pills to take at regular intervals.