Yes, you can become a Catholic at any age.
The general process that’s used is called the Rite of Christian Initiation of Adults (RCIA). RCIA consists of liturgical rites, instruction, becoming part of a parish community, and prayer. Some parishes – especially large parishes where they have a separate group for teens who are becoming Catholic – sometimes refer to this as “RCIT” (substituting “teens” for “adults” in the name).
Depending on the parish, you may be able to start RCIA at any point of the year, or they may have everyone start at the same time, usually in the fall. Ultimately the preparation will ready you for completing your sacraments of initiation (confirmation and the Holy Eucharist), usually at the Easter Vigil (the Mass the night before Easter Sunday).
A big question is how your parents feel about the idea of you becoming Catholic. If they’re supportive, you can call your local parish now and talk with a priest about all the details. If they’re opposed, that changes things because people here won’t advise you to defy your parents but to perhaps wait until you’re out on your own.
Welcome home!