Are staph infections and shingles related?

No. Shingles is caused by the chickenpox virus (varicella zoster virus), which is an entirely different organism from staphylococcus aureus, which is a bacteria. However, shingles lesions can get superinfected, and the most common cause for this is staph. Aureus.
HIV test suggested. Disease processes are different. However, recurrent skin/soft tissue infections with staph and development of shingles in a young adult should raise the suspicion for hiv. Since HIV weakens the immune system, staph and shingles signal the presence of HIV infection that is otherwise silent until CD4 counts approach 250 cells/mm3. Get an HIV test!