Seize, I don't think you had anything to lose by sending the gifts. In fact, you sent the gifts for all the right reasons -- it was about her birthday and giving her some nice things. No harm in that.
Probably time to move on though, in the sense that you have bigger fish to fry so to speak. You need to concentrate on yourself, and staying sober. There is all the upside in the world to that -- and part of the good could be getting her back. And even if not, you are in an infinitely better position than you were a week ago.
Going back to drinking? ALL downside, no upside at all.
And everything you are feeling is natural. But again, focus on yourself and taking care of yourself and getting healthy.