Liz, I had a very helpful conversation with an Al Anon friend a couple of years ago, when I was early in my recovery. My issue was balancing minding my own business and staying detached and staying on my side of the street, with my right to know the truth about certain critical issues that would have been determinative in whether I left my AH at that time (that is, was he cheating on me). After a good long talk, I reached a conclusion that at that point, I had decided that the alcohol addiction/abuse was not enough to make me leave my AH at that time. Any snooping or checking around about how much my AH was drinking, or under what circumstances, was just straight up unhealthy for me. And for me, about 98% of the snooping I was doing was related to me wanting to "prove" that I was "right" about the drinking, about being lied to, etc. But I also came to appreciate that if I learned that my AH was cheating on me, I would leave him immediately. So my Al Anon friend and I had a very practical, helpful conversation about keeping my "cheating radar" on, and not being afraid to follow up on something that was primarily evidence of cheating. In the end, with a lot of "two steps forward, one step back" progress, after about a year I had stopped virtually all of my snooping. I stopped, largely because I realized that the overwhelming majority of my snooping was not about following up on legitimate, real concerns of cheating, and because the snooping was causing me very serious physical distress. Rapid heart rate. Significant stress. Upset stomach. It just wasn't worth it anymore, and I came to understand that I honestly don't need proof of anything. At first, the proof didn't matter because I had decided I wasn't ready to leave (barring infidelity). Later, the proof didn't matter, because I became more comfortable with my feelings and didn't feel the need to justify them to myself or to others with "hard evidence." I don't have proof that my AH has cheated on me, but that no longer mattered. Obviously, if I was confronted with evidence that he is cheating, my feelings haven't changed: I would leave. But on a deeper level, as I have become more comfortable with the idea of leaving in general, I find that I don't need "proof" that I am "right."
I know I'm right. I know my feelings are valid and justified. I know that I have every right to want to leave my husband. And that's enough for me.
I sense that you have decided to stay in the marriage for now. And that is fine. Would abuse of prescription drugs (which, I agree, is par for the course with an addict, who will likely abuse whatever drugs he/she can if they are readily available) change your mind? Are you SURE abuse of prescription drugs would change your mind? If you have set a boundary about that, and are fully prepared to follow through with the consequences of crossing the boundary (i.e., leaving your AH), then I would say it might be worth the absolute minimum amount of investigation to determine if he is abusing the prescriptions.
But if this is just to be another thing for you to fret and worry about, but that will not spur you to action in your own life...another thing for you to WISH you could control, but can't...then I agree with other posters and try to bring your focus back to yourself, and your own recovery.
((HUGS)) to you, my friend.