The correct answer is (A) feeling.
"Had me feeling" is the correct structure — have/had + object + present participle — to describe a resulting emotional state.
The structure "had me ___" requires a present participle (V+ing) after the object pronoun. Options (B) "felt" (past tense), (C) "to feel" (infinitive), and (D) "feels" (third-person present) are all grammatically incorrect in this pattern. Remember: have/had + object + bare infinitive OR have/had + object + present participle are the two valid constructions, and context here demands the participle.