One thing that I am surprised no one mentioned is water intake. If your not properly hydrated and you come to a hill like this you will be sucking air. If you are properly hydrated your body will need less actual air to perform. SO proper hydration is very important for someone who is out of shape; more so than for someone who isn't. As for the chest pain, is soreness? When I first started riding my bike again I found that after a hard ride where I was breathing extremely heavy I would get so sore that it would hurt the next few days because the muscles used to breath were being worked harder than I had been used to.
Keep at it and it will get better, good luck.