My husband has a muscle knot in his back, a little tingling in his left arm (the side the knot is on), tightness in his chest, and shooting pain down his leg. His blood pressure is good. What could this be?

Anything. The most important thing is to get a diagnosis. Radiating pain on the left side demands ruling out a heart problem. One of my professors of medicine told us that pain from a heart attack can be anywhere from the teeth to the testicles. In other words even though the symptoms are not "classical" make sure that it is not a heart issue.
Pain back and chest. Many possibilities. Good idea for him to get checked up by your family physician to see what the problem (s) are and get proper treatment.