The other Carroll in 1820 Bedford County TN was James, not William.
Timothy Carroll had at least 10 children based on the 1830 census + the older sons, who had married by 1830.
In addition to Felix, John Milton, and William B., other sons were Aaron (died in Mexico as part of the Mexican War in 1848); Joseph died before 1854 in Coffee County TN; and Thomas died before 1838, when his son was named an orphan per the county court minutes. There may have been another son
According to the Yell researchers, James Yell married Jerusha Barton.
Rebecca Carroll was likely the daughter of James Carroll, i.e. a niece of Timothy Carroll.