Shortness of breath, indigestion, and general bloat are common in pregnancy, but what it sounds like you’re describing is more of a squeezing, which could be anxiety. Are you nervous about the whole situation, having problems? Pay attention to what’s on your mind or how you’re feeling just before the tightness occurs. If you notice it’s worrisome thoughts, try to "zone out" and relax or lie down, breathe slowly, and think about something pleasant and soothing. It might be a good idea to discuss it with your doctor in case it’s something more serious, though.