"Am I not supposed to think about him?" is not correct? What would it be in Czech, then?
I agree 'aren't i' is acceptable english whilst 'am i not' is a bit clumsy. I am a native English speaker
Also, the contractions are handled by Duolingo centrally for all the courses. We only enter non-contracted sentences for acceptance.
It wasn't accepted most probably because it should be "Am I not" instead of "Aren't I".
"Nemám na něho myslet?" The sentence is read by the speaker like a statement, not a question. Rising intonation at the end would make it clear that a question is intended.
And rightly so. nemám - I am not supposed to, nemusím - I do not have to, nesmím - I must not.