Lindsey, we really need to see a picture of this problem with the little tree. A little more of a close-up than your first picture would be good, and especially a close-up of the shriveling top leaves. If you can take the picture in the natural light, that would be good, too.
Are you using any fertilizer? If so, what kind and how often?
Citrus can take lots of water, as long as there is good drainage in the pot. They don't like to dry out especially if the weather has been sunny, so it's warm in front of that window during the day. Is that pot you have it in a clay pot? They are slightly porous so will dry out faster than a plastic or ceramic pot, too. I think the first thing to try is watering it more. Can you take it and put it under the shower or in the kitchen sink, and give the whole plant a good shower? Use slightly warm water, so you won't shock the plant, and spray the whole thing, leaves, stem, soil and pot. Get it good and wet, then set it in a spot where it can drain. If I had a citrus growing indoors, I'd definitely try to do this at least once a week. Then water once or twice more until water flows out the bottom of the pot, too.
They really aren't meant to be indoor plants, unless you have a big, glass atrium or a greenhouse. Even dwarf citrus get to be fairly big for an indoor plant, probably over 6ft. wide and high.
