I'm having pain in my back when taking a deep breath. Should I be worried?

Evaluation. Could be your heart, arthritis, slipped disk, herniated disk, kidneys, etc.. Get checked by physician.
Depends. If you are having pain in the mid back and/or rib cage area, you should contact your primary doctor. If the pain is severe or if you feel winded (cannot catch your breath), consider going to the nearest emergency room or urgent care center.