Catholic Church is Post-trib and A-Mill; always has been and always willbe untill the Lord comes back.
Clearly hasn’t always been.
In the first three centuries, the predominant view appears to have been premillennial.
Not dispensationalism, of course, but what evangelicals today call “classical” premillennialism (“classical” precisely because it has roots in early Christian teaching).
Perhaps the first three centuries is an overstatement, but certainly Irenaeus was a premillennialist, and he seems to be expressing the common view of the second-century Church.
Augustine is usually credited with popularizing the “amillennial” view.
I would question the priest who said that the Church teaches that we are in the millennium now. At least in other contexts, Catholics generally use the phrase “Church teaching” fairly narrowly, so you might want to be careful with it here. This is certainly the traditional view since Augustine, but I’m not sure it’s official teaching.
The Catechism condemns what it calls “millennialism,” but I’m not at all sure the condemnation actually applies to “classical premillennialism.” It definitely applies to postmillennialism, and on other grounds its pretty clear that dispensationalism is contrary to Church teaching. But I’m not convinced that classical premillennialism is unorthodox–in part because that would mean that most Christians for the first three centuries were unorthodox!
I myself do not have a strong preference between amillennialism and “classical premillennialism.” Dispensationalism and postmillennialism seem to me to be the two clearly erroneous views, erring in opposite directions.
The real question, I think, is the relationship between the Church and the Kingdom.
Edwin