Most LCD monitors give me major eye strain. The CRT monitors did at first until I discovered that when I raised the refresh rate up to 85, I was OK. Is there something similar with an LCD monitor that I can "tweek" or look for when going to purchase one? Would an LED monitor be beter for me?
LCD monitors generally has one or two sources of flickering that maybe causing eye strain for you.
Regardless if you are using a monitor with CCFL (florescent) or LED backlight, both of them flicker. Voltage PWM (pulse width modulation) is used to control the brightness. The brighter the monitor the less PWM is used. Technically speaking, at full brightness there should be no PWM, but actual full brightness may actually be too bright and will use too much power and shorten the lifespan of the backlight. PWN usually operates between 175Hz - 220Hz.
Most inexpensive monitor are made with TN panel monitors as opposed to VA or IPS which are used in more expensive monitors. Some inexpensive monitors are made with e-IPS panels to compete with TN panels monitors; but are slightly more expensive than TN panel monitors.
TN panel monitors can only create 256k colors. They use temporal dithering to create up to 16.7m colors. This is the reason why they are inexpensive to manufacture. Temporal dithering means if the TN panel cannot produce a color it must blend two colors to make it. For example, just assume a TN panel cannot create purple. What the TN panel must do is to quickly flash between red and blue so that your brain registers purple. This also applies to e-IPS panel. I don't know at what frequency temporal operates at, but this may also cause your eyestrain. Therefore, TN panel and e-IPS panel monitors have two sources of flickering.
VA (PVA, MVA) and IPS (S-IPS, H-IPS) panels can truly create 16.7m colors without having to use temporal dithering. This is part of the reason why they cost more to manufacture which means a more expensive monitor. Therefore, LCD monitors using these panels should only have on source of flickering; the backlight.
60Hz monitors vs. 120Hz monitors
I don't think a 120Hz monitor would help you vs. a normal 60Hz monitor. The 120Hz technically allows up to 120 frames per second to be displayed on the screen. This great for gamers, but not much of a big deal outside of games.
Unlike a CRT monitor which uses an electron gun to excite pixels one at a time from the top of the screen to the bottom of the screen, the pixels in a LCD monitors remains "excited" until it needs to change colors which is why LCD monitors do not have a refresh rate. Additionally, all 120Hz monitors use TN panels.
The best solution, might be to spend money on a more expensive monitor that uses a VA or IPS panel. A 24" monitor using one of those panel technologies starts at about $425 - $450 and will go up from there. There is no guarantee that this will not give you eye strain. You should also not focus on the monitor for hours on end. The "20/20 rule" state for every 20 minutes of usage, look away from the monitor an focus on a distant object for 20 seconds before looking at the monitor again.
your issue is most likely with the backlight. there are four options available to you:
-use a monitor that when at 100% brightness does not use PWM and instead keeps a constant on backlight. you can then dim this with a monitor "screen" or possibly even through software-based graphic options (though not sure about this second one)
-a diy fix that uses incandescent bulbs to produce a non flickering backlight. search the forums for a post that references this as there is a user on here which acomplished this.
-follow all of the recommended safety tips for monitors. this includes taking breaks, using a comfortable resolution and having ambient light around you at all times. not flourescent lighting if you can help it as the ceiling panels often flicker alot.
-use a CRT monitor instead. most go up to 85hz or more and they are still available although probably by special order.