Becoming an official catholic?

My parents were never married, but have always lived together (and still do). Growing up all of my cousins and relatives were catholic. They were baptised, confirmed, and so they were able to do things like get married through the Church and have quinceaneras (we're Latino).

I've always admired Catholicism despite some of the negative coverage it gets in the media (the stereotypes of pedophile priests and what not). Since I am technically illegitimate my parents never bothered to baptise me, and of course without being baptised I couldn't move further in the process.

I am an adult now (21) and at a Jesuit University so it's possible for me to start going through the process. I know some prayers like "Our Father" and "Hail Mary" but I'm embarrassed to go to campus ministry because I'm not a virgin. I've only had one sexual partner, but it was premarital nonetheless. I was reading up and it says you cannot be confirmed if you have committed a mortal sin.

Should I not mention that I've had sex before? I mean technically brides who are not virgins are not supposed to be married in white but it happens all the time. I feel guilty about not being a virgin. Now that I am in a serious relationship and an adult I don't want this shame (one of being "illegitimate" and two of not being able to partake in things like confession) to bring me down anymore. I really want a catholic wedding, and I really want to be an official catholic for the rest of my life.

Is it still possible for me to go through the motions (ie: RCIA *Rite of Christian Initiation for Adults*) and become an official Catholic recognized by the Church even though I am no longer a virgin?