Regularly wearing high heels can result in shortening of the calf muscles; a thicker, stiffer Achilles tendon; ankle instability; and increased pressure at the ball of the foot. High heels also change our center of gravity with resultant knee, hip, and/or back pain. The problem when running with these physical changes is the decreased flexibility and quicker fatigue which can result in the arch pain that you have been experiencing.
My recommendations: Find times throughout the day to perform foot and leg stretches and kick off those high heel shoes as often as you can. If your symptoms persist, see your podiatrist for a proper diagnosis. Many of my patients with these symptoms have found relief by wearing prescribed custom orthotics when they run.