At the end of the story, what makes Montresor feel sick?

Although Montresor states that it is the damp air of the catacombs that makes him feel sick at the end of the story, Poe hints that Montresor's sick feelings represent remorse for his actions. Consciously, Montresor is in denial about the monstrous nature of what he has done, feeling justified in seeking his revenge, but that doesn't mean he doesn't subconsciously experience guilt. 

Why might Montresor's feeling of sickness be from guilt or remorse? First,...

Although Montresor states that it is the damp air of the catacombs that makes him feel sick at the end of the story, Poe hints that Montresor's sick feelings represent remorse for his actions. Consciously, Montresor is in denial about the monstrous nature of what he has done, feeling justified in seeking his revenge, but that doesn't mean he doesn't subconsciously experience guilt. 

Why might Montresor's feeling of sickness be from guilt or remorse? First, we discover he is telling this story 50 years after the crime, possibly on his deathbed as a confession, suggesting it still weighs heavily on his mind. Second, he says about Fortunato at the very end of the story, "in pace requiescat," Latin for "may he rest in peace." This indicates that Montresor, if he is not being ironic, has forgiven his former rival. Further, up until this point, the dampness of the catacombs only bothered Fortunato, not Montresor. There's no physical reason for the air to suddenly make Montresor feel sick. In a short story, every word counts: Poe would not include this sickness detail for no reason. 

Finally, Poe was a master at intuitively understanding human psychology, especially the psychology of guilt, as we see in stories such as "The Telltale Heart." Montresor has been excited all along about achieving his goal of revenge, but like many who achieve their heart's desire, at the point of victory the triumph may ring hollow or the person may have second thoughts. Montresor's feeling of sickness correlates too closely to the end of communication with his friend (whether by death, because Fortunato passed out, or because he refused to speak) to dismiss it as merely physical and not, at least possibly, to the consequence of guilty feelings.