This problem through which you are suffering has become very common among people who have to work long hours on the computer. I will suggest you to get your eyes checked by an ophthalmologist to get sure if you do not have any vision problems. Many people do not have any problem with LCD screens. The doctor may prescribe for you glasses that will give relief to your eyes even if you do not have any vision problems.
You should adjust the colour, contrast and brightness of your monitor to help your eyes get comfortable, you can adjust the glare, make the colour of the walls at the place where you work dull and see to the lighting to which your eyes are able to best adjust with.
Sometimes the symptoms may also be related with sleep. Do you sleep well. You should sleep for atleast 8 hours to let your eyes and head get relaxed. Do work out with your bed room, make it a cool pleasant place to retire. Put new curtains, freshen up the wardrobe, change your mattress and have a good each day.
Exercises are the most important part to get rid of your symptoms. Take short breaks while you work. Sprinkle water on your face and eyes to feel fresh at intervals. Perform head, shoulder and eye exercises each day. When you get a little free try doing it also at your work place. Close your eyes and massage
your eyelid gently the muscles will get relaxed. Try doing the exercises for your eyeball muscle relaxation. Go to an expert or a gym to take the tips.
Improve your diet, keep yourself hydrated, take fruits and berries rich in vitamin A
and C. Since you have a sedentary job eat low fat, high protein diet and exercise regularly. Take care.