Here is where his battery served:

This command was organized at Mobile on 16 October 1861, with men and officers from that city mustered in on the 31st. The battery remained in the defense of that city until the spring of 1862 when it moved to Corinth. It was in the Kentucky Campaign losing lightly at Munfordville (Sept 14-17, 1862), and none at Perryville (Oct 8, 1862). It suffered severely at Murfreesboro (Dec 31, 1862-Jan 2, 1863), where it was in Manigault's brigade. At Chickamauga (Sept 19-20, 1863), the battery was engaged without loss; but at Missionary Ridge (Nov 25, 1863) it lost three guns, and half its force was captured. The other half were distributed in Cobb's (KY) and Mayberry's (TN) battery (January 1864), and served till the end.

Griffin was marked present on the Jan 1 to Apr 30, 1862, muster roll. Jul 1 - Oct 31, 1862, he is marked absent sick. (This does not mean he was sick the entire time, but that was his status as of Oct 31). Oct 31 - Dec 31, 1862, shows the same status. Dec. 31, 1862 - Feb 28, 1863, is more specific saying that he was "Absent sick since 14 Nov 1862 by authority surgeon." This would indicate that he most likely came back to his unit during the two week period from Oct. 31 to Nov. 14, but was sent away (we know not where) by the surgeon. We then find him discharged at Rome on Apr 2, 1863, "incapable of performing the duties of a soldier because of Phthisis Pulmonalis (a tuberculosis of the lungs with progressive wasting of the body). My guess is that he died very soon thereafter, possibly still in Rome, as he was likely too weak to travel. We do not see a date of death, only that a quartermaster received what money he had ($13.15) on May 30, 1864. This money could have been held by the surgeon for some time before being turned over to the quartermaster. Since Rome was still behind the lines, it is certain that he was in a Confederate hospital. I cannot make out the name of it, but, although it does look like it starts with "P", I do not believe that it says "Prison Hospital". Perhaps someone with greater knowledge of hospitals in Rome may have that answer.