Looking for Chalagatee, also George Brewer

I have bits and pieces of family history and for years have intermittently tried to learn about my Cherokee bloodline. My grandmother (my father’s mother) was Lula Mae Avery Kelley, b. 1888. I have been told we are descended through her mother Nancy Lucinda Graham Avery, b. 1853. My uncle told me many years ago that he went visited a Cherokee archive site and found out we are descended from Chalagatee, b. 1780s?, whose english name was Brewer. He is listed as one who went out west in 1817? He showed me a copy of a page he got from the archives where my grandmother Lula Avery Kelley registered (a role?) along with all the children she had living at the time, which was the mid 1920s. Her husband is not listed, I’m assuming because he wasn’t a Cherokee. I am trying to trace back through my grandmother to Chalagatee and fill in the blanks to find out who is in-between and if Chalagatee is my 4x great-grandfather. My father and his 11 siblings grew up in Oklahoma. They all physically resembled American Indians.