Tom's cough was chronic my dude... Lol jk, but it is chronic.
The central conflict and its resolution in "To Build a Fire" is:
c. The man is in conflict with the extreme weather; the conflict ends when the man freezes to death.
Even though the man had conflicts with other characters in the short story, their conflicts arise from the central conflict of man needing to learn how to build a fire in order to keep warm amidst the extremely cold weather.
Just take what you are going to talk about it your paper and summarize it. Make sure to put Down's Syndrome in your thesis though since that is the main topic.