The Ready State Virtual Mobility Coach is like having a virtual Kelly Starrett in your pocket.
The clicking in your elbow could be crepitus of the tendons caused by inflammation. If you have full range in the elbow/wrist (extension/flexion and supination/pronation) then mobilization won’t necessarily help. However, voodoo flossing them will definitely help with the pain and clicking, but it won’t fix the underlying biomechanical problem. Make sure your technique is flawless and that your elbow tracts directly under your wrist when you press, and that you have sufficient torque on the bar at all times so your joints don’t get improperly loaded.