Yes, possibly. The upper lip, back and chest are all areas that are prone to breakouts. If you have a tendency towards ingrown hairs and irritation from shaving, you are more likely to have the same reactions waxing, although dramatically decreased. To minimize skin reactions, you MUST use proper home care and come to get waxed on a regular schedule.
All-in-all, come in like clockwork, every 4 weeks on the dot, exfoliate your skin and moisturize. This will help set you up for waxing success!