It would depend a bit on WHICH unspecified tire you have.
Tires with extensive (relatively speaking) "flat protection" would likely be more resistant to "failure".

IF you have a new tire, use some kind of caliper and measure how much thicker the new tire is.

At 3000 miles, you have gotten your money's worth and a new tire provides more peace of mind.

If the tire still seemed in reasonably good condition, I'd probably put a patch on the inside to cover the "roughness". No sense having it possibly compromise the tube.