My eyes may be dry. I spend a lot of time on the computer, and when I go outside, my eyes get sensitive. Heavy eyelids, watery eyes, redness. Help!

Yes. You describe classic symptoms of dry eyes. However, you need to determine if you have a quantity problem (not making enough tears) or a quality problem (making tears that are not stable and readily evaporate off the eye) or both. Your eye md can help make the correct diagnosis and offer the appropriate treatment.
See an Eye MD. In your age group dry eyes are less common than blepharitis, a condition were the oil producing glands become inspissated their orifice closes possibly related to stress. Then the extra oil cause heavy eyelids, watery eyes and redness. Another possible reason can be uncorrected significant astigmatism. Please see an ophthalmologist for correct diagnosis first.
Try artificial tears. This is a very common problem with heavy computer use. Artificial tears over the counter are very helpful. Stay away from generics and brands like visine and clear-eyes. Systane, refresh, genteal, theratears, and blink are all good brands. They are safely used 3 - 4 times per day. If your symptoms persist, see an ophthalmologist.