Hand washing is great! It is one of the best ways to prevent the spread of illnesses... but yes, there is definitely such a thing as too much. Your skin is one of your bodies best sources of defense against the environment and if you wash your hands so much that they are cracked that's a risk of infection on its own.
I'd probably think about where the anxiety is in control VS good hygiene & see if you can manage to cut back. At home for instance, washing your hands constantly is likely doing you more harm than good.
Of course it's not always easy to simply stop something that is anxiety driven or has become habit so I would maybe invest in a good glycerine based lotion for your hands too to keep them healthy.