Thank you for your help!!
They should be able to show you where the tire was punctured even if what caused it is no longer in the tire. They have a water tank they dunk the tire into that shows where the hole is by the bubbles.
If you buy a new tire take the old one with you and search for the hole on your own.
Another way a tire can pop is by hitting a pothole hard enough to where it pops the bead and deflates.