Here's the proper posture for running, look forward to the horizon when running make sure that you do not bend forward or look down. Just keep your body erect and your face and jaw relaxed. Keep your shoulders relaxed, do not creat tension by tightening them.
The ideal posture is running tall as track and field coaches describe it.
Swing your arms forward and back while running and keep them close to the body. Your hands should not cross the midline of your body.