Your birthday star is in the constellation Draco. It is called 26 Draconis in the Historia Cœlestis Britannica of John Flamsteed and Edmund Halley. It is called NS 1734+6152 A in the NStars database.
It has visual magnitude 5.3 meaning that you could just see this star with the naked eye under the best viewing conditions. It is marked in the center of this star chart, at celestial coordinates (J2000 equinox): Right ascension 17:34:59.6 Declination 61:52:28.4
This star is 45.9 light years away, which means that the light we see from it today set off on its journey at about the same time that you were born.