The short answer is no, water cannot burn. This is because a fire requires three things in order to burn, 1) a fuel (like a piece of paper or a log of wood) 2) an oxidizer (oxygen gas in the air is usually the oxidizer in a fire) and 3) heat or a source of ignition to kickstart the chemical reaction of burning.
Interestingly, water actually is the byproduct of hydrogen combustion, which does happen. During this reaction, the hydrogen and oxygen atoms fuse together to form a molecule of water. Since free molecular hydrogen and oxygen atoms have no valence electrons, they instantly bond with each other to form covalent bonds, releasing energy in the process. Then, the oxygen atoms can move on to find other molecules with which to bond, such as free molecular hydrogen or oxygen.
Since the chemical process of burning involves breaking apart existing bonds, it takes a lot of energy to get something to burn. This is why putting water on a flame puts out a fire; it smothers the fire by blocking the oxygen from reaching the burning molecules in the fuel.
When it comes to burns, the best way to treat them is to keep the skin moisturized with a water-based lotion or aloe vera. You should also gently wash the burned area daily with cool water to remove any contaminants from the skin and prevent infection. Over-the-counter pain relievers like ibuprofen and acetaminophen are also helpful in alleviating the discomfort caused by a burn. If you suspect a serious burn, see a doctor immediately for proper treatment and care.