If you aren't locked in to a specific pharmacy, you should be able to pick up your prescription at any pharmacy that takes your insurance. CVS will tell you if you're locked in to another pharmacy when you try to get it filled. If it's during normal business hours, they'll call your insurance company to get an override so you can pick it up from them. Being locked in to one pharmacy & having to get an override usually only pertain to controlled medications though.
Usually you can do that if it's not controlled substance. You'd need to call to arrange it
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