The basis for married women's hair covering in the Torah is that the kohen uncovers the sotah's hair (Bemidbar 5:18), from which we may deduce that married Jewish women kept their hair covered. This law is further discussed in the Mishna and Talmud.
Although halacha obligates married Jewish women to cover their hair, there is a range of opinions on how much hair needs be covered and in what manner. We urge you to inform yourself about this halacha and the many different ways of adhering to it. Being informed can help you find a way to observe this mitzvah that is consonant with your sense of self.
To this end, we recommend the book called Hide and Seek published by Urim Publications. It is a collection of essays, primarily by women, on hair covering, with a halachic summary in the introduction.
For an English-language discussion of the relevant sources, we recommend the first chapter of Understanding Tzniut, by our rabbinic supervisor Rav Yehuda Henkin (published by Urim). Also of interest by Rav Henkin is Responsa on Contemporary Jewish Women's Issues (published by Ktav), chapters 16-17.