Your "some kind of anxiety" is social anxiety disorder, or SAD, possibly with agorophobia (you'll have to clarify how "afraid to leave the house" you are). Whether or not you'd be eligable for a card is up to your doctor, but he'll have to be pretty open to it since there's no way to accurately measure the symptoms, prove that you have SAD that is, so there's a good chance of your doctor thinking you're just trying to get high.

Good luck man.