Misty, I am a descendant of Sarah TEAL & her first husband, Zachariah MARTIN and I don't think your Tom BURNEY could be a descendant of Simon BURNEY & Sarah TEAL. They left Louisiana in the 1820s and settled in Grimes Co., TX. I only know of two sons, William & James, b. 1801 & 1804 respectively.
Since your Tom BURNEY had Georgia forebears you might begin with Elizabeth (CHEEK) BURNEY's presence there:
The Families of Burke County, [GA] 1755-1855 a Census; compiled by Robert Scott Davis, Jr. and Rev. Silas Emmett Lucas, Jr.
Pg. 19: Burney, Elizabeth.Granted on March 3, 1767.Grant Book F, page 94. 300 acres on the north side of Buckhead Creek and bounded on the west by land of James Howell and on the south by Buckhead Creek.Granted to Elizabeth Burney during the term of her natural life and from and after her decease, to her son, Simon Burney.
Burney, Elizabeth.Granted on January 5, 1768.Grant Book G, page 3. 100 acres bounded on the southeast by land laid out for a township and on all other sides by vancant land.
Burney, John.Granted on August 2, 1768.Grant Book G, page 150.150 acres bounded on the west by James Bowie and on all other sides by vacant land.
Pg. 20: Burney, William.Granted on August 4, 1767.Grant Book F, page 310.150 acres bounded on all sides by vacant land.
Burney, William.Granted on April 5, 1768.Grant Book G, page 68.150 acres bounded on all sides by vacant land.
Pg. 96: Burney, Elizabeth, Sept. 1765, from Orange Co., N.C., lately to Ga., has 6 children, asks for 300 a., no side Buckhead, 2 mi. of Jas. Murphey,; Aug. 1766, for son Simon Burney, granted 300 a., next Jas. Howell on Buckhead Cr.; Mar. 1767, granted 300 a.; Jan. 1768, widow, granted 100 a.
Burney, John, Aug. 1768, granted 150 a., next Jas. Bowie.
Burney, James, Feb. 1768, granted 150 a. next John Burney.
Burney, Richard, Jan. 1784, granted 100 a.
Burney, William, Jan. 1767, has wife and 3 children, asks for 150 a. Rocky Comfort Cr., near Peter Grant; Aug. 1767, granted 150 a.; Apl. 1768, granted 150 a.; Nov. 1770, with Reason Whitehead, asks to purchase 500 a. on Big Cr., next Wm. Burney, to build a sawmill.
As you can see, there were several sons, any one are all of whom could have remained in Georgia after Simon moved to Louisiana. Hope this helps. Bob