Do I have to convert to Judaism if I have a Jewish mother?

My father is a Muslim and my mother is Jewish (she's now been a Scientologist for a few months but I'm sure she'll grow out of that phase soon). Anyway, I was raised with my cousins, who are devout Christian nutjobs (the kind who think you're possessed by the Devil if you're gay). So I had the unfortunate experience of a Christian upbringing. I'm now 18, I'm in college, and I've completely left Christianity. I left it two years ago and my cousins made me leave the house so I went to stay with one of my friends from high school who was from a Jewish family. So anyway, I'm really interested in being Jewish but I'm not sure if I'd have to go through a "conversion" officially because I wasn't raised Jewish. Do I have to do the conversion or am I okay to just call myself a Jew and join the religious community because I have a Jewish mother? I'm interested in Reform. Possibly conservative.