Everyone here echoes the importance of NC. I agree, and also advise you to accept HER doing NC to you, for your closure, as I have been dumped enough to know that you may never know the reasons they dumped you, because they don't know.
Until you have had to dump someone, its just hard to understand the concept of feelings changing for no apparent reason.
Never send holiday, birthday, or any other day, greetings. If she acknowledges it, you wonder what it means, and freak, and if she doesn't acknowledge your greeting, you wonder what it means, and freak! So don't do it. True NC, is No Contact whatsoever.