Weight charts average around 123 - 163 for your height, depending on your frame size and your BMI is 23.5 to 24.5 (just within the healthy range). It may not be that you need to lose weight, but need to redistribute it through exercise. Work on the spare tire part with abdominal exercises.
As for running, start off with what you can do. Buy a good pair of running shoes/socks and start out slowly to see what you can do and work up from there without over exerting yourself.