2000 Toyota Tacoma Vibration After New Tires

Bought four new tires same size as previous set. Tires were balanced and mounted, but vibrates while driving. Had tires rebalanced 6 times, same results. Mechanic said the rack and pinion needs replacing as well as the shocks. Prior to replacing tires, had one tire come apart while driving on interstate (70 mph). The spare did the same, only it blew out causing damage to the fender. Could this have caused damage to the rack and pinion? The truck was driven another 150 miles after blowout, without this vibration.