You mentioned that some of the things this girl has said have made you doubt your Catholic faith. That is a bad sign. But it can be corrected with prayer and God's grace.
If you are Catholic, you must pray the Act of Faith regularly (preferably daily). Make sure, as you say the words of the Act of Faith, you understand what you are praying. Meditate on what the words mean. Then study whatever traditional Catholic Catechism you find most helpful. The Catechism of Trent is the best in my opinion (but it may be too advanced for some). There are many good Catechisms freely-available online. Make sure you know your Catechism well before discussing the faith with that girl again.
Until you can pray the Act of Faith honestly and can say that you know the Catechism, you should not talk to that girl about religion. If you have real "faith" that the Catholic teaching is the Truth, then nothing that girl can say will ever change your mind.
If you get to that point, it will then be a prudential decision whether you talk religion with her again. If you think she is open to converting to the Catholic Faith, then maybe you can ask her to read the Catechism with you. If she is not open to converting, don't talk to her about religion.
And do not read a Protestant Bible translation. Those Bibles have many errors in them. Stick with the Douay-Rheims. And definitely do not become romantically-involved with a non-Catholic girl.
THE ACT OF FAITH
O my God, I firmly believe
that you are one God in three divine Persons,
Father, Son, and Holy Spirit.
I believe that your divine Son became man
and died for our sins and that he will come
to judge the living and the dead.
I believe these and all the truths
which the Holy Catholic Church teaches
because you have revealed them
who are eternal truth and wisdom,
who can neither deceive nor be deceived.
Amen.