Wow, you sound a lot like my partner, and your girlfriend sounds a lot like me. She has the same insecurities as I do. It has led to fights before. Maybe 3 or 4 in 3 years time. For myself, when I end up projecting something like envy (he's really hot and passes much better than I do), it's because I can't ignore it anymore. I tried, though. but that's not very helpful to you, I'm just sharing...
You are awesome for not blowing up at her - that must have been difficult. What I would like my partner to do for me, when I get obviously envious is focus on me for a little while. Let me cool off, course. Let me have a half-day of space (that's just me, if she doesn't like space, then maybe don't wait) then the next day, or sooner, slowly become extra cuddly and/or attentive for a while. For a while, I would want him to just sleep with me, but not begrudge me for it, and also continue to tell me how hot he thinks it is when I'm getting picked up by another person. If you can, I suggest waiting to fool around with someone else until she does. But if that's too long a wait for you, then don't bother. Just give her some extra lovin's - she sounds like she wants to feel super special. Remember, the world (especially ads) is telling her she's never good enough, just like the world tells us we're never masculine enough. (Patriarchy's an ass, hey?) I personally believe it's our task to boulster self-esteem/confidence in our partners when it's low - just like what you already do. I'm saying that perhaps individual attention can do this better than even the most heartfelt words.