I have had this deep chest cough with shortness of breath for a week. she went to the doctor and her blood pressure was 157/134 should i be worried?

Yes: She needs to follow up on the blood pressure and have more readings done. That diastolic number is ridiculously high. Please schedule a follow up appointment asap.

BP high: That BP is a little high, I assume your doctor checked you out for possible heart disease/conditions. Also, hopefully you are not a smoker which can also result in cough and elevations of your BP. I wouldn't be worried unless your BP continues to be elevated on multiple occasions so I would make sure I return for close follow up with your doctor. Good luck!