Ceiling Light Flickers
I am guessing that you have copper wires, right? Not aluminum, right?

Replacing receptacles is almost certainly not necessary. If your receptacles are connected with push-in, "back wire" connections with spring connections not screws, then an over-current event may have burned and loosened the connections. If your wiring is done that way, then changing the wires to the side screws would be strongly advised.

The fact that you can affect the light by banging on the wall indicates that the problem is in a wall receptacle (most likely or in a wall switch box (less likely but still possible). 

You would need to check all the receptacles on the circuit. If you are providing care for a person with special needs, it might be best to call an electrician to fully check out the circuit. Electrical work can be dangerous and if you were to be injured you might not be able to perform the essential work you are now doing.