I'm not sure, long distance is tough, but my general goal for a good relationship, is that honesty and openness fuels a good relationship.

If he's not willing to accept you AND your depression/social anxiety... I HATE to say it but it might not be right. It should NOT be the focus of the relationship. But it would make him understand. Just a thought, but I dunno anything about the two of you or your relationship so take this with a grain of salt