The correct option is B eating
Here, the gerund 'eating' is correct. The main verb in the sentence determines whether to use a gerund or an infinitive. 'Ill' requires a gerund 'eating'. If it would have been something like 'likes', then 'to eat', an infinitive, should have been used. Both gerunds and infinitives can be used as the subject or the complement of a sentence.
'Being eaten' in present continuous tense is an incorrect usage because the sentence uses 'felt', not 'feels'.
'Eaten' in simple present tense is incorrect because the sentence uses 'felt', that is in past tense.