In Danish, there is the word »rask« (I am sure there are similar words in other Germanic languages), which means either 'not sick' or 'quick'. The latter sense is largely context dependent, and considered a bit old fashioned.
The advantage of the former meaning, is that one can ask »føler du dig rask?« (approx. 'do you feel not sick?'). I wonder if there is a word in English to convey the same meaning in a single word, so you can formulate the same kind of polar question.
The word 'healthy' (as in, 'do you feel healthy?') could also imply you lead a healthy lifestyle. One can be not sick, while also being unhealthy.
Similarly, the word 'well' (as in, 'do you feel well?') - while closer - could also imply different meanings, as it has different connotations. English is a second language to me, but I still have hard times grasping the exact meaning of 'well'.
And I feel, at times, that native English speakers have the same problem. If someone asks, 'do you feel well?', and my financial situation is looking bleak, and it's worrying me, but technically I do not feel sick, I would probably answer 'no'. But if someone asked me 'do you feel not sick?' in the same situation, I would answer 'yes'.
Am I misinterpreting the word 'well'? Or does English lack a clear singular word meaning 'not sick', that has broad consensus in terms of meaning? In Danish, since »rask« is an infrequently used word, its meaning is generally agreed upon. Unlike 'well'.