Dear Ms. Meziere,
Thank you for posting on History Hub!
The National Archives and Records Administration has numerous records relating to Choctaw land allotments including some that deal with applications that were not approved. A list of series is available here: https://catalog.archives.gov/search?q=choctaw%20allotment&f.level=series. The records are available at several different NARA facilities. You would need to contact the individual facility directly to access the records.
The Choctaw Nation has a handy information sheet on their website that discusses how to research your Choctaw ancestry. We suggest you look at Census records in order to find the parents' names. We also suggest you try to get a copy of the marriage record which may also give the parents' names. FamilySearch has a webpage on Rapides Parish, Louisiana Genealogy. In your inquiry you mentioned that you visited the Rapides Parish Courthouse. It might be worth checking for all marriage records for the mid 1800s containing the family names.
We hope this information is useful to your research!