Sorry, but I do not think your ancestor was at Andersonville.
There is a grave for J Covey, died 4 Aug. 1864, at Andersonville National. Grave 4683. Find a Grave Memorial 51153139. (Find a Grave lists him as J Covey). That grave was registered as J Covey, Pvt. 38th ILL. INF.
Andersonville records list him as: Carey, Joseph L. Alternate spelling Covey. Private, Company A, 38th Illinois Infantry. Captured at Chickamauga. Died of scurvy, 4 Aug 1864.
Illinois Adjutant General roster records list Joseph L Carey, Co. A, 38th. Captured at Chickamauga. Died at Andersonville.
I doubt the FAG Memorial for J Covey is your ancestor if his surname was Covey.