Depends on what's wrong with your eyes. But probably not. Computer monitors can cause more nearsightedness, because of the physiology of your eyes. Your eyes are meant to constantly adjust itself, so that it should be constantly refocusing on items of various distances... looking at your hands, the person next to you, the table across the room, the bird out the window, etc, etc. What a computer monitor does though, is reduce all this refocusing, so your eyes is staring at a single point in space (the screen) for long lengths of time, sometimes even hours without ever looking anywhere else. Eventually this sort of behavior will start reducing the 'elastiscity' of your eyes, so it can't 'focus' on distant things as well.
An LCD won't help with this sort of problem. There are other problems computer monitors can cause though, but the best person to answer these type of questions, and that you should have asked, should have been your optomistry when they brought up the problem.