I was intrigued by this post as I am descended from John Flowers, born John Barrot or Barrett, who along with his brothers was born out of wedlock the generation before Elizabeth, also in the Bladen/Robeson county area.
There is no one named Barrot or Barrett in either Robeson or Bladen county NC in 1810, when your Elizabeth was a girl. There are two Barrotts, John and Isaac, both in Rowan co. NC. I can't find a single Barrett/Barrot on the 1820 NC census. Either she moved there from out of state, she was from Rowan county (a fair distance from Robeson), or something else is going on -- like she'd had a shortlived marriage to a Barrot and went by her married name, or went by a stepfather's name. I even entertained the idea she was a daughter of my John or one of his brothers (he seems to have had several brothers. I know of William and Wright for sure, and there seem to have been two more, Drury and Arick, based on deed evidence). But they all changed their surnames in the very early 1790s, so if she were born prior to that she would have been nearly 30 when she married. Not impossible.