Why is my car making a clicking noise from the rear wheel area while driving?

Clearly sounds like a brake system component that you removed making noise. Perhaps brake pads are moving in the caliper bracket? Retainer clip issues? Many guesses, but hands on inspection is needed. You've gone as far as taking everything apart and verifying the noise is gone - you'll need to dig deeper to witness what is making the noise with the components reassembled. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops