Let me join Mike in welcoming you to the family, even though you aren't officially in the Church yet.
Mike is correct in that you will need to be baptized.
I didn't realize Unitarians even baptized anymore but, in any event, it was more than likely invalid. Unitarians, because they joined with Universalists, denied the Trinity. So it's unlikely that your baptism would have had the proper Trinitarian formula with the intent to perform Christian Baptism. Unitarian Universalists self-identify as non-creedal. Meaning that you don't have to believe anything in particular to join their society. In fact, officially they aren't a church or Christian. Hence the name Unitarian Universalist Society.
You will need some instruction prior to Baptism. Mike referred to that. It's called Rite of Christian Initiation for Adults or RCIA . You will need Godparents, but they may call them sponsors.
They must be Catholics; one male and one female.
Because you are only 17-years-old, I'm not sure whether you will need parental consent but, in any event, you will be 18 in a year. RCIA begins in the fall and culminates with entrance into the Church at Easter so it's probably too late for this year. It's likely the priest will want you to go through the whole program, especially since you're coming from sect that, unlike many Protestant denominations, is not considered Christian.
The good news is that you can still attend Mass and pray with us. You can participate in everything aside from receiving Holy Communion. When others go up for Communion, you can ask the Lord to commune with you spiritually, and you can go up and receive a blessing from the priest.
O Lord Jesus, I believe that You are present in the Most Blessed Sacrament of the Altar.
I love you (above all things with all my mind and my heart) and I long for You in my soul.
Since I cannot receive You now sacramentally, at least come spiritually into my heart.
I embrace myself entirely to You and unite myself wholly to You.
Never permit me to be separated from You.
Optional add-on: Come Lord Jesus and glorify Yourself through my weak body.
If we can be of any other assistance, please let us know. Please stay in touch with us.