That is a very astute question for a bar mitzva, one which shows that, already at your age, the study of Torah is not a new mitzva for you. There are two possible reasons to make a Shehecheyanu when beginning to put on tefillin. One is that the performance of the mitzva is new, as you imply. The other is that the tefillin are a new, important commodity (no less than a new suit), which brings joy even to one who has put on other tefillin for years. According to both reasons, the time to make the beracha would not be the day of the bar mitzva, but the first time one puts on the tefillin. This is usually before the bar mitzva, each young man according to his minhag.
The Rama[1] states that one says Shehecheyanu the first time he does shechita (ritual slaughtering) – not on the shechita itself, which causes damage to a living thing, but on the mitzva to subsequently cover the blood. Based on this, the Taz[2] rules that whenever one does a mitzva for the first time, he should say Shehecheyanu. However, many poskim take issue with the Rama and/or the Taz.[3] The main rationale of those who take issue is that, since the emphasis of the beracha is on our meriting being alive at this time, the mitzva must be one which is linked to a certain time of the year and, thus, be cyclical. This difference of opinion may depend on the understanding of the baraita, cited in Menachot.[4] [5] The baraita relates that the kohanim who came to Yerushalayim to bring the mincha (meal offering) would recite Shehecheyanu. Rashi explains that this refers to the first time the kohen ever brought the mincha, and this would seem to support the Rama and Taz. However, Tosafot[6] says that kohanim made the beracha each time because the kohen had the privilege to do so only twice a year, making it a cyclical mitzva. As we have a rule that safek berachot l’hakel (when in doubt whether to make a beracha, do not possibly utter HaShem’s name in vain), we do not make a Shehecheyanu on first-time mitzvot.
However, there is room to say that there is special justification for reciting Shehecheyanu on tefillin. The tosefta[7] says that when one makes tzitzit or tefillin, he makes a Shehecheyanu, and this is stated as halacha in the Rambam.[8] (There is discussion as to when the beracha is made, and we usually make berachot at a later point than the classical sources indicate.[9]) The Tur, though, cites this tosefta only in regard to tzitzit, not tefillin. The explanation appears to be that, according to the Rambam, the fact that tefillin and tzitzit are mitzvot makes their acquisition significant enough to warrant a Shehecheyanu. The Tur disagrees because only cyclical mitzvot require the beracha. He agrees that tzitzit calls for a Shehecheyanu because it is at least an article of clothing.[10] Since tefillin are not clothing,[11] their acquisition is not of material significance.
The Shulchan Aruch sides with the Tur, and the accepted minhag among both Ashkenazim and Sephardim is not to recite Shehecheyanu the first time one puts on tefillin or on the bar mitzva. However, the Mishna Berura[12] and Kaf HaChayim[13] both suggest that one put on an important new garment and say Shehecheyanu right before putting on the tefillin for the first time, having the tefillin in mind as well, to cover the doubt.