Tina, let's talk about this.
I believe that the Eleanor Adamson that married Joseph "Herrin" is a different lady entirely and he did not die young. I do think you are definitely on the right track. Simon Adamson [1763-1814] and his wife Eleanor Routh [1769- aft1860] and their family lived in Jefferson Co, TN. I believe their youngest daughter, born probably about 1813, just before the death of Simon, is the Eleanor, called Ellen-not Nellie, who married Joseph, whose name was actually Hearn, not Herrin. Now Simon only mentioned his "younger children" in his will, and so this Eleanor does not appear in all databases. She would have been about 16 when she married Joseph - works well. In 1860, Collins County, TX, the family of Joseph Hearn and Eleanor can be found AND her mother, Eleanor Adamson is living with her, she was age 91. So that effectively removes that Eleanor and her husband Joseph - she cannot be your Eleanor, your Nellie. Other siblings of this Eleanor are in Collins Co, TX as well.
Of course, John N. Adamson and Mary Hammer also had a daughter Eleanor [her birth recorded in the Quaker records in 1804] and they lived in Jefferson Co TN As far as I know these are the only two Eleanors in this time and place in this particular Adamson family. John & Mary Hammer Adamson's children scattered a bit, but certainly their son Seth, just younger than Eleanor went to Iowa.