Had a similar incident on the 737-400 MMGL to LAX. We didn't blow the tire, but threw the tire cap. Never knew about it until I was doing the walk around in LAX and spotted a skid mark on the fuselage by the R2 door.
I wondered how that got there until I saw the tire minus all the tread. When we asked the F/As if they heard anything on takeoff they said one passenger mentioned it but only spoke Spanish so they weren't sure what he was talking about.
The shredded tire cap did some damage the flaps. Aircraft was out of service for 3 or 4 days. The Captain and I had no idea anything happened until we caught it visually.