Hi
Welcome to the forum!
Well a low back injury cannot cause symptoms in the upper part of the body, except when a clot travels up and blocks a blood vessel. Usually the symptoms are below the level of the injury.
As SurgiMenopause mentions, you must rule out angina or heart attack by a 12 lead EKG first, maybe if not at the doctor’s then at an ER. The other possibility of such a pain is gastric reflux or GERD. At times costochondritis (inflammation of the joint between chest bone and ribs) too behaves this way. Do discuss this with your doctor and get yourself examined.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!
I believe you should go to the ER and make sure you did not just experience a heart attack. It can make you short of breath, give you pain in your shoulder and chest, as you may know as well as affect your hand. You probably have heard they can happen even to young people, and it is better to be checked out than not about something so serious. If it's something else, hopefully, the doctor at the ER will try to assist you with what that might be. Blood clots are also potentially life threatening, so with the warmth in your arm, it is best to go to the ER and get it checked out because if a clot breaks loose, it can potentially go to your lung or heart, etc.!