Bhavin,
According to date of birth you may be libran but that is the western style of calculation, as per Indian Vedic system your Moon is in the 9th sign which is Sagittarius and hense your Rashi is Sagittarius. In Vedic astrology we follow the Moon and not the Sun as in Western Astrology. Just for your knowledge Yes Librans and Geminis are highly compatible not only because Venus the lord of Libra and Mercury the lord of Gemini are friends but they are in the friendly distance as per astrology analysis and any libran would click very well with the Gemini. The only things to note here is that Librans are more balanced while Gemini sign as twins can be quite fickleminded and two personalities. I hope it helps you find a good compatibility.
God Bless,
Navneet Khanna
astrologer