I don't think TN had births records in 1828 but you don't know where he was born in TN so that option is out.
I'd look for his marriage to Matilda and order a copy of their marriage license. Their parents might be on it.
Also check the local newspaper for their marriage announcement. Their parents might be in it.
1850 Yaobusha Co., MS
Thos I. Neely, b. TN, 24, planter
Matilda, b. TN, 16
Ann E., b. TN, 40
I think Ann was his mother.
He would have died before death certificates were used (started in 1912). You can contact the Benton County Health Department and ask if they have any earlier death records.
Generally the local genealogical and historical society has a local death index, old newspaper and cemetery inventories. The Northeast Mississippi Historical & Genealogical Society, http://nemshgs.blogspot.com/
covers Benton County but I don't know if they're active or not.
Mississippi University, http://lib.msstate.edu/specialcollections/collections/geneal...
has records regarding Benton County.
You can look through the newspapers at Library of Congress, Chronicling America for his death notice. His parents names might be in that. Successful Searching!