We probably are not directly related through your grandfather, Herman Aaron. Do you know anything about his lineage? How far back can you trace the Aarons in your family?
Aaron (and its variants) appears to have been a common given name (first name) among members of the Jewish faith. However, the Germanic Aaron variants (such as Aron, Arendt, Arons,Ahrens, and Arendt) are primarily surnames (family names). This is where we might share a common link.
Your grandfather would have been born in approximately 1862. Because I can trace my paternal lineage (with names and dates) all the way back to approximately 1779, I know that your grandfather (Herman Aaron) is not in my direct lineage. However, there is a possibility that I am descended (directly or indirectly) from a Johann Arens, born in Frackel, Germany, in 1570. Johann Arens might be our common ancestor, because Johann and your Herman were German Aarons. Genetic markers estimated for Johann Arens (displayed at the online Aaron DNA Project) are reasonably close to my genetic markers, suggesting a reasonably close commonality.
Has any male in your direct lineage been tested, genetically? Approximately one year ago, I connected with someone whose wife and I are direct descendants of the William Aaron born in approximately 1779. We do not know his birthplace. However, we do know that this William Aaron lived in South Carolina and had two sons, John (born in 1800) and Richard (born in 1803). I am a direct descendant of John, and this woman is a direct descendant of Richard.