The answer is not a cut and dry one in your case. The troubleshooting is a process. You will need an understanding of a multiple light parallel circuit. You will also need a proximity type voltage tester and possibly a VOM.
Assuming the voltage feed starts at the switch (not always the case, but normal) you will need to verify input voltage at the line side of the switch with the switch in the off position. If you have voltage there, turn the switch on and verify voltage on the load side of the switch. At this point, a VOM is handy to test voltage across the hot and neutral and/or ground. If this looks good, proceed to the closest light fixture, and with the switch on, test the center hot tab in each fixture with the no-touch tester. In your case I would think you may not see any voltage based on your question. This could mean that you have an open neutral, an open hot, or at worse, a shorted hot to neutral/ground.
Since there are several possible reasons for your condition, it would take a lot of tutorial to explain every possible scenario. Assuming you do not see voltage at the fixtures, the basic technique for troubleshooting will be to start at the last known verified voltage point, then follow the wiring and check all connections in the junction boxes. Visually check the bulb sockets for broken or shorted metal tabs. This should be done with the power off at first, looking for obvious loose or disconnected wires, then with the power on using your voltage tester. Since this condition occurred after you adjusted the height of the sockets in the fixtures, I suspect tension on some wire may have pulled a wire out of a socket base or out of a wirenut in the j-box. Unfortunately, most can/pot lights have a built in j-box attached to the top of the fixture. This necessitates dropping the fixture down below the ceiling to access the j-box, or getting access from above. (attic).
Basically, you are following the circuit looking for an open or short, just like following a hose, looking for a water leak or stoppage.
This is not a hard job, but extreme caution must be taken when testing energized circuits. If you do not have good electrical skills, the proper test equipment, or a logical understanding of switched paralleled circuits, then this job is better left to a pro.
Maybe one of my buddies here on SE can add a good graphic showing this type of circuit and the test points. A simple line drawing showing the switch and junction points would be a great edit.
When you say "ceiling" I take it to mean a fixture lens or diffuser. All fluorescent lamps put out light at a high frequency that can be bothersome to some people. This frequency is determined by the ballast, which will vary by manufacturer and lamp type. The actual shape of the fluorescent tube makes little difference in the frequency unless the ballast is changed as well.
Diffusers and reflectors tend to mask the high speed off/on effect that is bothersome. Directly seeing the bare tube will more likely be bothersome than any other configuration. You've also dramatically changed the light dispersal pattern of the fixture by using CFLs in place of the intended halogens. This could also be why the new configuration is making you uncomfortable. Another factor could be the CFLs are putting out more light than the halogens did, amplifying the effects from other factors.
You might consider LED lamps that come in smaller packaging and may more closely replicate the dispersal pattern achieved by the original halogens. If you want to stick with CFLs, consider using those where the tube is encapsulated by an integral diffuser.
![enter image description here](https://i.stack.imgur.com/TOiJP.jpg)
Best Answer
I doubt that you damaged the fixture. You probably loosened it from the electrical box it's attached to. Usually the bulbs can be changed without removing the fixture from the wall. Turn the light off (because it gets very hot) and try to push up the fixture and rotate it in the opposite direction to correct what you did before. Get a ladder, not a chair, and get up there close so you can see what's going on up there and where the bulbs are.