Your girlfriend is wrong, unfair, and completely out of line. Men will look and have sexual thoughts... it's natural... it's expected... and she needs to learn to accept this. Further more... it is completely wrong to guilt someone into doing what you want --- which is what she's doing to you --- and I sympathize with you completely.
Furthermore, every woman I've ever met looks at others and occasionally or even often (depending on the woman) they may have sexual thoughts involving someone (porn, strangers, friends..etc) other than their significant other. This is also natural and expected.
So pull out the porn, look at the pics, and enjoy those fleeting thoughts when you look at some attractive woman passing by for you are a guy... and this is what you do.
She has some growing up to do and possibly some insecurities to work out. Make no more promises and if she asks why or demands that you do... remind her that you cannot promise to do the impossible, and she really has no right to control your thoughts and emotions anyway.
"The weakest soul, knowing its own weakness, and believing this truth that strength can only be developed by effort and practice, will, thus believing, at once begin to exert itself, and, adding effort to effort, patience to patience, and strength to strength, will never cease to develop, and will at last grow divinely strong."
- James Allen