The OP is “really married” in the sense that the Catholic Church will not make an investigation of nullity for a marriage that has not been dissolved in the eyes of civil authorities, whether that dissolution takes place via civil annulment or civil divorce. In other words, as far as the Church is concerned the OP is not free to marry (anyone other than the person they’ve contracted a civil marriage with) because the OP is in an existing marital contract that is recognized by civil authorities. That’s a sort of “real,” I suppose.
The OP, being Catholic, is required to follow Church laws with regards to marriage. Therefore, the putative marriage is in need of convalidation to meet the objective standards of validity. In that sense, the process of becoming “really married” isn’t finished for this couple yet, let’s say that. The OP needs to see his/her pastor to see what it will take to accomplish that. In that sense, the couple is not really married yet, no.
Therefore, with regards to marriage, the OP is in a sort of a limbo between that is neither free to marry anyone else that is free to marry in the Catholic Church nor validly married in the objective sense. The OP has started the process required to get married, has given up the freedom to marry anyone else in the course of that process, but has gotten the cart before the horse and done things in the wrong order.