Possible Electrical Short After Drywall Installation
This sounds like a rather dangerous situation. The drywall installers no doubt did not install metal straps on the studs wherever an electrical wire crossed through the stud. Most likely a drywall screw or nail has gone into the stud and entered a wire that crossed the stud in the same place. 

The fix for this may require a professional electrician unless you are pretty familiar with electrical wiring work. It will be necessary to cut the power to the circuits and open all the applicable electrical boxes and disconnect the various lights, switches and power feed wires. Then shorts checks can be made using an appropriate ohm meter for all the wires in the area between the boxes. 

Once the short is located it will likely be necessary to remove the drywall in that area to replace the wire. 

Do not leave this problem go. It sounds like you have a medium resistance short in some wire/stud crossing. I say medium because you did not mention that it is tripping a breaker. The resistive short can produce a lot of heat and could definitely lead to a fire in your wall or ceiling.