It’s not a “refresh rate” really. LED’s are Light Emitting Diodes, and a diode is an electrical component that only allows electricity to flow in one direction. So an LED only works when electricity is flowing in one direction. Houses run on AC current (Alternating Current) with a frequency of 60Hz in the US. So if you plugged in normal AC into the LEDs, it would be off half the time, flickering 60 times a second. The LED light bulbs should have built in components that convert the AC signal into a constant DC signal. If you get normal bulbs that are well made, there should be absolutely no flicker.

Are you using a lot of computer screens at work? Because using computer screens can cause eye strain, and also cause you to blink less resulting in your eyes drying out. Both of those can cause headaches. If you do use a lot of computer screens, you should consider getting eye heat compress (my ophthalmologist recommended me this one). You should also be able to get normal store bought LED bulbs that do no flicker. Perhaps try the slightly more expensive name brand options if the store brand isn’t working for you.