What is wrong with my back and arm?

I would definitely suggest that you get in to see your doctor as soon as you can. Any pain that is persistent like this should be checked out to make sure it is not a serious problem. I suggest that you start with your primary care doctor. Most of the time, low back pain, especially when it is on one side only, is related to a strain or a spasm of the muscles on that side of the spinal cord, known as the paraspinal muscles. This most typically happens because of bad posture or heavy lifting. Fortunately, it is not usually a serious problem and it can usually be sorted out with back stretching and strengthening exercises as well as anti inflammatory medications under the guidance of your doctor. I am concerned by the pain spreading up the side of your chest and also the trembling in your arm. I am not sure if this is just related to an overall stress reaction to the pain in your lower back, or if it means you have a more serious problem, but I think that a good physical examination with your primary care doctor is the best place to start.