The use of "felt" in that context usually indicates a possibility that maybe she was not sick. She just felt sick.
But if that student is so deeply into the study of English as to really have a feel for individual words, such like you are indicating here, she/he is an exceptional student and you had better be an exceptional teacher to guide her/him along.
Let me give you another example of the use of 'felt' in that sort of context.
It felt strange. --- compared to --- It was strange.
The first we could state is conjecture and the second is fact.
Or:
I feel you are going to be a good student. / / / I know you are going to be a good student.
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