Yeah, enough sleep should take care of that.
You get baggy eyes either because you're genetically prone to get them, dark veins are more visible under your skin or when fluid starts to accumulate under the skin. That could be caused from poor eating (salty foods) or just being tired.
Try using the apple, potato and even cucumbers. Tea bags (try chamomile) can help you too. Just soak them a bit and sit back with them on your eyes. Tea has tannin which acts like an astringent to help reduce the puffiness. If any of these aren't available, put a couple of tea spoons in the freezer and when they're sufficiently cold, put them over your eyes to help reduce the swelling.