Will acne spread from one area of my body to another?

No. The processes involved with acne formation can occur in many places over the face and body. They don't spread.
Can occur elsewhere. Acne occurs on the oily skin areas (where the sebaceous oil glands are), which includes the entire head and neck, the upper back, and the upper chest. The conditions needed for acne already exist in those skin areas, so acne doesn't truly "spread".