If you are sure of your Jewish roots, but were unaware of them until now, all these years you were considered akin to a tinok shenishba (a babe who was taken into captivity, referring to your spiritual world). It is wonderful that you are reclaiming your heritage and it is best to look to the future. Focus on study and beginning to practice the laws and traditions, rather than look back. You are not held entirely responsible for not acting like a Jew if you did not know you were one.
Jewish law today does not encourage a single woman to immerse in a mikveh until just before her wedding. Traditionally, prayer and tzedakah (giving to the poor or doing good deeds) are considered no less purifying to body and soul then immersion in a mikveh.
However, there are places which permit unmarried women to go to the mikvah for purification and teshuvah (repentance) purposes the afternoon before Rosh Hashana and/or Yom Kippur. At that time, you could check your local facilities.
We wish you much hatzlachah (success) in discovering the beauty of Jewish life.