As far as the size EUR44 for men, they do exist (some brands even go as small as a EUR42 eg. Dior Homme, DSquared---though admittedly the 42 is probably to allow the female demographic to wear the clothes with an appropriate fit....such as Cate Blanchett, who used to wear Hedi Slimane designed Dior Homme). I own quite a large number of jackets in this size, OtR, from a range of different designers. But then, i'm based in Asia, where such a small size is actually quite in demand.
So i wouldnt rule out the tux jacket being from the menswear collection on size alone. However, other members have already chimed in with the observation that the general cut and proportions of the jacket not being really standard TF menswear, which might suggest it's a womenswear item (I have no experience with the Tom ford cut, given it's not available in my country....so i really couldnt say based on my own experience).
Having said that, one question would be, would you be able to fit into a EUR44? It would seem a moot point if the jacket were too small for you anyway.
On the other hand, if you're fashion forward, and the jacket fits your frame, i dont see why you couldn't wear it for NYE? (Unless it's a fear of being self-conscious and wondering if people are snickering at you behind your back and saying "Look at that fool wearing a woman's tuxedo jacket!!!")