The thing is, you can't really have OCD without the anxiety. The reason for the checking etc is usually down to the anxiety behind it. So it isn't really a new diagnosis for you. Incidently many doctors have OCD tendencies, the worry of keeping their hands clean between patients. It only needs treatment if it is causing a problem for you and disrupting your life.

If the anxiety and depression are treated then the OCD should get better. Hope you have a therapist to help you.