Hello. Thank you for coming to JustAnswer with your question, and welcome.
It is highly unlikely that water gives you headaches. More likely, the headaches are caused by drinking less of the diet soda or other things you prefer especially if they contain caffeine. These types of drinks are really not good for you. Diet soda has been found to cause weight gain in people as well as regular soda and other sugary drinks.
Your body needs hydration, and water is the best source. If you do not like the taste of it, you can add some fruit juice (lime, lemon, peach nectar, etc) to flavor it. But you should definitely drink more water and less of the other things.
You should gradually change from your routine fluids to more and more water, until you are drinking about 2 quarts of water a day. Other healthy fluids would include real fruit juice, though it should be diluted and used sparingly because of the natural sugar content. Milk, lowfat or nonfat (2-3 cups per day) for the calcium/magnesium and vitamin D it contains. And herbal teas, just because it is a good way to get in more water without sugar and caffeine. If you need caffeine, there is nothing wrong with a couple of cups of coffee per day, or better--green or orange pekoe tea.
Headaches can be caused by a lack of water or dehydration. But if you are not used to drinking an adequate amount of water, it will take you body a few days or so to adjust to a more normal fluid intake.