my experience with waxing my chest was 6 years ago. I did it at home with one of those pre-wax strips kits. It was painful, but it did the job. My chest is fairly sensative, and I break-out every so often when I shave. I didn't break out at all after waxing, however I wasn't able to get all of the hairs. It is also tough to wax around the nipples (at least in my experience). If I remember correctly, it lasted for a good 2 weeks or so. It is my understanding that it would have been far less painful and a far better job had I gotten it professionally done.
Here is what I would suggest for you:
Since there is no way for anyone to predict how your chest would respond to waxing, I would (if I were you) give your chest hair a few days of growth after shaving your chest so the hair is roughly 1/4 inch long. I would buy a waxing kit from the store and test patch a small area on your chest. Wait 24 hours and see how your chest reacted. If there isn’t a breakout in 24 hours than I would say you’re in the clear to have it professionally done. Since you don’t leave town for almost another month, I would think you have plenty of time. Also, test patching an area of your chest at home will give you an idea as to how long waxing will last for you. The duration varies for different people. For all you know, waxing may not last long enough for you to even consider the time, expense, and discomfort of a professional wax.
Those are my unprofessional thoughts.