Even though Sheridan does not appear on any 'official' records of the 13th VA Infantry (that I have been able to discover), it seems as if he may have served with that regiment at Gaines's Mill where he was wounded. The letter writer mentions Sheridan, Reuben and Conway Newman being wounded there.
With Sheridan not enlisting in the 60th Tennessee until October 1862, this just adds weight to his prior service.
I will have to keep searching for some other 'unofficial' but period verification of his service with the 13th VA Infantry.