Anna,
I've only worked on a small number of units in my research. There were quite a number of Pickens men in Ferguson's/Beauregard's Battery of Artillery. Company officer Lieutenant Henry D. Calhoun recruited heavily in the upstate and drew many men from Pickens county.
I think, but don't know, that Pickens would have been in the area from which the members of the 2nd Infantry Regiment were drawn.
How about some family names?

Glenn