Are you able to access your UPS account without integrating with Shopify? If so, it has to be a problem with Shopify. Maybe you can try generating shipping labels directly from UPS and see if it works. Alternatively, you can try our Multi Carrier Shipping Label app with a 14-day free trial if the issue doesn't resolve. The app lets you connect your UPS account and display the rates, generate UPS label and automate the tracking process.
Hope it helps you!