Drinking water will help with dehydration, not dryness. Dehydration is lack of water, dryness is a lack of oil.
Your moisturizer might not contain enough moisturizing ingredients. You should be looking for ceramides, hyaluronic acid, niacinamide, fatty alcohols (like cetearyl alcohol) and glycerin. Possibly petrolatum too. I find most moisturizers usually just contain the basic glycerin, petrolatum and maybe an oil or two. Sounds like you need more.