I was christened as an infant in the Catholic faith. Due to where I lived, a Catholic church was not available, so I attended a Baptist church. I married a Catholic man, when we went to mass with his family, I was told by his family not to partake. It offended me but were they in the right?
I would say they erred on the side of caution. Your baptism is fully valid in the Catholic Church and since you are mature enough to distinguish the Eucharist from regular food you have every right to partake.
However, because you were raised in a Baptist church, you did not receive a Catholic education nor did you have a Catholic confirmation. (In fact the Baptists do not Confirm since they do not baptize infants.) I also assume that you did not perform the sacrament of penance before taking Communion. Therefore, you partaking could present the appearance of impropriety. If you intend to continue worshiping in the Catholic church you should discuss taking the Rite of Christian Initiation for Adults with a priest. This will include education, Penance, Confirmation, and Communion.
If your family had been able to keep going to the Catholic Church where you were Baptized (christened isn't what Catholics call the sacrament, but don't worry about that. A convert friend of mine just posted pictures of my daughters "Christening" on Facebook, I was like, hmm when was that?) Anyway, if you had remained in the Catholic Church you started out in you wouldn't have automatically been able to receive Holy Communion until you had finished the preparation (usually happens I the USA by 2nd grade), but it wasn't always like that, in other times and places First Communion might not happen until the communicant is a teenager.
But you've got nothing to worry about, if you want to receive communion go to the priest and ask him what to do, it's not a one-size fits all problem.
A validly baptized infant is a Catholic until he/she acquires the age of reason and rejects a tenet of the Catholic Faith (Dogma), when this happens a person becomes a heretic and is at that point is a non-Catholic. If you are going to a Baptist church you've definitely rejected some Catholic Dogmas.