Hello and welcome to JA.
How did you bleed the air from the system? What procedure did you use?
OK...on 4.7L...whenever the cooling system is serviced, the air MUST be bled from the bleeder fitting which is located on the engine, right next to where the upper radiator hose connects. It requires an 8mm hex tool to remove the bleeder fitting. I learned this by witnessing another tech learn this...the hard way.
The system will never burp the air out otherwise.
I hate to be the bearer of bad news, but in most cases, when the engine overheats to the point that it runs poorly and makes noise, usually the engine has sustained serious damage.
It does. The next step is to properly bleed the cooling system and retest for proper operation. The shop should check the usual things: thermostat, flow through the radiator, fan operation, etc. One thing that should definitely be done is a head gasket test. Any decent mechanic should have the inexpensive tester to perform this test. It uses a special fluid to check for the presence of carbon monoxide in the coolant, which would indicate a faulty/leaking head gasket.
Typically what happens is: engine overheats due to low coolant or another problem. This overheating causes the engine metal to expand too far, which creates a head gasket leak. The head gasket leak allows combustion gases to enter the cooling system, leading to 'air' pockets and additional overheating.