Late for the party but I'm poly and I had this exact conversation with my boyfriend yesterday. We end up talking about people we wouldn't want the other to date, something like a veto. It's perfectly normal to have this boundary because the boundary is where you feel uncomfortable ! And I would feel the same as you !
Turns out my best friends as well as his best friends are "out of limits" because we would struggle too much with those exact feelings you're having. And your girlfriend knows this, she asked you to be honest with her which means telling her what you told us.

I feel trapped between having to choose between something that makes me hurt inside to just think about, and denying two people I love the chance at something that could be great.

If you're hurt by their hypothetical relationship, your already great relationship with your gf would probably suffer from this ! Ask her if she would resent you for not approving of a romantic relationship between her and your best friend !

Feel free to PM me