It sounds to me like she really over reacted and may be incapable of having a relationship with you.
This is not your fault, I think the premises for your relationship was built on a faulty ground, only this brought it to the foreground. Of course you notice attractive women! And your “response” was very normal for all men, especially in the under 30 crowd.
All people are attracted to attractive people! If that was not true, why would movie stars have such followings. It is not just single women that follow Brad Pitt like a panting dog! “As for only drunks and babies tell the truth” concerns me. She does not want you to be honest? What is she hiding? You should tell her she should be happy you can’t lie! That way, you could never cheat, or really even “think” about cheating without her knowing.
My husband, 2 days before we got married, went out for a night on the town with some friends to say goodbye to the single life. They went to a few strip clubs, got drunk, and the one friend wanted to go to a rub and tug. My husband was very upset. The friend was MARRIED! He came home, and the next day, told me! He just could not keep it to himself! I was happy to know, and noted he moved away from that “crowd” as soon as we got married. He has not even been to a strip club in 6 years!
Best of luck, if this all blows up, try not to blame yourself. One comment like that should not set a solid relationship falling like a house of cards unless the foundation is really faulty. I am sorry you have come to see just how fragile the relationship is. Kudos to you for keeping it going so long!