iPhone 13 ‘peeling’ along the edges of the back. Best course of action??

Yes it’s potentially dangerous and it should be taken to an Apple Service provider ASAP. You can also contact Apple Support. If you’re in the US please call  1-800-MY-APPLE or outside the US, consult the support articles below.

Contact Apple for support and service - Apple Support

Genius Bar Reservation and Apple Support Options - Apple

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zaye04 wrote:

Hi,

My little sister’s iPhone 13 is having serious issues it keeps switching back and forth between the Apple logo screen, and the side of the phone looks like it’s coming apart. It seems like the battery might be swelling, which is really concerning. According to reddit this is a explosive issue

Should I take it to an Apple Store or AT&T for repair? Which option would be easier and more cost-effective? I just paid the phone bill, so I’d prefer not to spend a huge amount if possible. Would they even recommend repairing it, or would they just suggest upgrading?

Thanks for any advice!

In addition to everything Jeff suggests, it should also be powered off and stored in a safe place until it can be seen at the Apple Store Genius Bar. Back it up, then power it off.