Your birthday star is in the constellation Pavo. It has the name ä (Delta) Pavonis in Johann Bayer's Uranometria star catalog. It is called NS 2008-6610 in the NStars database.
It has visual magnitude 3.55 meaning that you could see this star with the naked eye in good viewing conditions. It is marked in the center of this star chart, at celestial coordinates (J2000 equinox):
Right ascension 20:8:43.6
Declination -66:10:55.5