in the most dangerous game why did rainsford most likely say he wasnt feeling well

Rainsford suggests he is feeling ill during his and the General's first night together after Rainsford is caught on the island. Simply put, Rainsford is shocked by the General's confession of his man-hunting enterprise. Seeing in Rainsford an adversary worthy of his skill, the General shares details of his game, wherein he hunts captives for sport. Rainsford, knowing he is at his host's mercy, having been left behind by his ship, does not want to too strongly deliver his moral outrage and perhaps upset the General, but neither does he want to hear more about this atrocity. So he pretends to be ill and is sent to bed, which of course only postponing the inevitable, which will be his inclusion in the General's game.

You know I don't recall this. He swims for his life when he falls in the ocean. When he gets to the island he just falls into "the deepest sleep of his life". During the hunt, Rainsford has a rough time. He finally felt like the hunted, "I will not lose my nerve. I will not." As for feeling ill, I could not find where you mean.