Can an infected bug bite first diagnosed cause shingles or is it not a bug bite but a single shingle and days later several blisters down your right arm and shoulder that I could feel burst?

The bug bite will not cause shingles. Shingles is a re-activation of the chickenpox virus that affects a single nerve bundle, generally on the torso.

The symptoms you are describing could be shingles (particularly if you had chickenpox as a child), or it could be an infection in the lymphatic system (possibly caused by a bug bite).