you haven’t given much information about your great great grandmother so that someone might help you with specific information.
no dates, no location, no children, no spouse in your post.
first, you might ask the tribe to send you a copy of her enrollment application and census card. other sources would be http://www.nara.gov fort worth office, oklahoma historical society http://www.okhistory.org/ or possible http//www.footnote.com
you can look her up using accessgenealogy and click to the footnote entry for that record, however, footnote might have a membership fee. i don’t know because i have never done that myself.
if she was alive 1/1/1937, she would have applied to social security and probably would have submitted a birth certificate or delayed birth certificate as proof of age.
several states have archives for old records.
each person in your lineage would be a separate record. however if someone in your line has already submitted records, then there are fewer records to submit. so you should definitely contact the tribe to see exactly what they need.
genealogists use names, dates, locations, children and spouses to match records. if you have a common surname, you need to give more information rather than less. if you post about women, it is helpful to include the maiden name and the married name and designate which one is the maiden name.
first of all, heritage and tribal enrollment are two different things. many times natives didn’t apply for enrollment because 1) they didn’t qualify, 2) they were philosophically opposed to enrollment, 3) they didn’t have documentation, or 4) they were mississippi choctaw and their ancestor had accepted land or benefits in lieu of tribal enrollment.
the dawes roll was taken 1896-1906, so you should trace your ancestors down to that time period. mostly, they had to be living in oklahoma by that time and agree to live there permanently.
if the name is common, you may find too many possible records.
the tribe has an excellent information to help you. it is found under genealogy advocacy.
http://choctawnation.com/services/departments/community-services/
mississippi choctaw and choctaw tribe explained here:
http://en.wikipedia.org/wiki/Choctaw_Trail_of_Tears
i have collected many resources over the years. if you want to write to me, shamlet76@gmail.com and request the choctaw resource list, i will be glad to send it to you.
i am just a volunteer that wants to empower people to learn how to do genealogy.
suzanne hamlet shatto