Arch pain with flat feet usually comes from a combo of shape mismatch and impact. A shoe that's narrow through the midfoot and stiff under the arch can press where you need room and flex and and pavement makes every step feel harsher. Thicker socks won't change that geometry enough to help.
If you can exchange them and look for a roomier fit through the midfoot and forefoot, a softer underfoot feel, and a shoe that bends where your toes bend. A specialty running shop can watch you jog for a minute and steer you toward shapes that match your foot. You actually can also try lacing that reduces midfoot pressure by skipping the eyelets over the highest part of your arch and using a heel lock near the top.
Give your feet a gentle ramp-up even with better shoes. Start with easy 10 to 15 minute runs and build by a few minutes at a time, mix in grass or a track to reduce pounding, and do light calf and arch stretches after you run. If the ache doesn't settle within a couple of weeks of these changes, get a proper fit assessment. Small changes add up.