Oh, shush. My boyfriend is 5' 11", I'm 6' 1". I wear heels as often as I like. He loves it! Haha, he even told me once, "Don't tell anyone, but I kind of like that you're taller."
Made me all sorts of happy on the inside. :)
If your girlfriend is having a hard time walking in heels, she shouldn't be wearing them. One of my biggest pet peeves is when girls who can't walk in heels, wear them. They take practice! And the right kind of heel. I just bought a new pair that probably makes me around 6' 4"-6' 5". They're my new favorite. And I can walk just as fast in those as I can in sneakers. I have heels that are more comfy than my running shoes. It is possible, I promise.
And you contradicted yourself in your question. "Don't tell me I'm insecure, but I need to feel like I can protect my girl!" I'm sure you're quite capable of protecting your girl. She's still the same girl in heels/flats/sandals/whatever. Whether you want to admit it or not, not being cool with her heels IS insecurity. Be proud she's tall! Instead of feeling sorry for yourself, try this:
When you guys go out and she (OH NOEZ!) wears heels, see if there are any other guys checking her out. And when you find that they are, look at them and make sure they know that that sexy woman next to you is in fact YOURS, and they may not touch. It makes her feel good, and you'll feel like you're protecting her. Know what I mean? :)
Once you can get past the idea that you HAVE to be taller, things get much nicer. You can enjoy -her- instead of worrying about her height.