hmm , talk about a rock and a hard place..

I can kind of see the conflict from both angles, you & your privacy but also your job and responsibilities there..
I would guess it shouldn't be too much of an issue until you return to work and depending on what meds you were on at that time.

But I think because of your ICU duties at least your manager or supervisor should be aware of any meds you are still on when you return to work. {This would be classified as extremely confidential information}

Does the hospital have rules about nurses/doctors being on certain medications, like narcotics? You might double check what the policy is in that regard, you don't want to violate something that way and be terminated for not disclosing medications.

those are just my thoughts
nice to meet you