Thanks to all who contributed. I agree with the advice offered, i.e. instead of signaling I wanted (to pay for) an upgrade to C mid-flight, which is complicated indeed for a number of reasons, the better approach would have been to emphasize the seriousness of how I felt at that point in time, and to have accepted the offer that they ask whether there's a doctor on board so that an ad-hoc solution could be found based on medical grounds, and upon the doctor's independent medical advice, instead of upon the wrongful impression I may have created that I wanted to get a freebee upgrade to C based upon "I feel sick" statements only I could vouch for in terms of their being genuine.
The thought of me being the one for whom they page whether there's a doctor on board was just a bit too intimidating I think to have accepted their offer. Interesting to read that a call for a doctor won't necessarily entail diversion. This is what I was worried for.
On the other question: when the pill was offered to me, no explanation was given indeed. I did not push the question either, since I was uncomfortable just taking a pill I did not have any further information on.
Feel free to continue to weight in. Very helpful thread. Hope I won't need the advice in the future :-)