I m Sephardic from my father who has passed away when I was two. I always felt Sephardic. But I really started to become religious thanks to a Chabad rabbi and I started to put tefillin daily after a Chabad rabbi showed me how to put it. I kept the tradition to put Chabad way. I used to go to a Chabad house but I moved and started going to a Sephardic shul now and the rabbi told me I should put the tefillin the Sephardic way as I’m sepharad. What do you think?
You should wrap the tefilin the sefaradic way, but there's no need to acquire new tefilin.