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Your birthday star is in the constellation Pegasus. It is called 85 Pegasi in the Historia Cœlestis Britannica of John Flamsteed and Edmund Halley. It is called NS 0002+2704 A in the NStars database.
It has visual magnitude 5.8 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 0:2:10.2
Declination 27:4:56.2
The light we see from it today set off on its journey at about the same time that you were born. Come back in a month or two and your birthday star may change, as the light from more distant stars reaches Earth.
