If she really DIDN'T want no contact, she would have thanked you for your reply to her birthday note. Or she'd send you a note. Or like something on your Facebook page. Or ask a non-business related question.
I can guarantee you that she does NOT want to be reminded of your affair, no matter whether she wants full no-contact or if she wants to be casual about you being out of her life.
Me42, H40 D12, S8, S7 A revealed: 7/13 Sep 4/14; Agreed to D 1/15