Hi, welcome to the forum,
Causes for
dry skin are Sjögren's syndrome (also presents with dry mouth, cheek swelling), Mucin deficiency, Amyloidosis, Sarcoidosis, HIV infection and uncontrolled diabetes mellitus.
Hence, you need to undergo blood sugar, salivary mucin content etc. to rule out the cause. You need to use moisturizing cream on the skin, drink adequate fluids and drugs like low dose steroids will be helpful for above mentioned conditions.