Call me the denomination cop, but the Catholic Church is not a “denomination”. Never has been, never will be. Rather, she is Christ’s Church. In her, He prayed for unity and one mind. He did not pray for unity with heretics.
The denominations are protestants who left the Catholic Church. Protestants left the Catholic Church, protesting the Church, and now represent the many different forms of protest to the Church.
Stop right there. You're misinterpreting the exact same passage of the bible that every other Catholic does, and what I myself as a Catholic once did.
Jesus Christ did not build His church on Peter. Jesus Christ built His church on the TRUTH that Peter Spoke.
You are a denomination whether you like it or not.