If it's painful for you to stand on your feet all day, definitely look into comfortable and/or orthopedic shoes (your health insurance may even cover them if they're medically necessary).
If that doesn't help - are you behind a counter all day or are you out on the floor? If you're behind a counter, even for part of the day, perhaps you can get a bar stool or chair that would allow you to sit down but put you at "standing height"? The chair would be behind the counter, so customers wouldn't necessarily see it. If it's a choice between that and your quitting, I'm sure your manager will agree.
Good luck with whatever you decide.
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