Dear One:
The real question I suggest you consider is: Whose crap is this ?
Your girlfriend has the courage to admit that is her issue and from what I read from your account, she is not avoiding your question.
What she is really telling you is that she loves you.
And that she feels shame to have performed oral sex with another man.
Can you hear this ?
So, do not make it your issue.
Let her work it out.
Finally, if, as you say you do, you do love your girlfriend,
then love her where she is.
Power has no place in a loving relationships.
You cannot make her give you oral sex, neither can she force you to do whatever. This is not an even transaction, it is not a powerplay, it is simple human pleasure.
Personally, I find great pleasure in giving pleasure to someone I love.
No compensation, no return of the favor, no conditions, no nothing needed in exchange of the pleasure.
Love is a gift you give.
I wish you Lots of Love