That is it! I am a blonde!

Whether or not you have problems with the "turning green" also depends on the kind of chemicals your pool uses.  My hair is naturally blond and when I swam as a kid there would be a slight greenish tinge by the end of the summer.

Now, I lighten (dye and bleach) my hair and haven't had any of those problem with the green thing.  I also think it's cause I take better care of my hair now, better shampoo etc.  From your pic, your hair looks really short, so you probably wouldn't have any problems anyway, the greeness only happened on the bottom part of my hair, and my hair was fairly long at the time.  There's also a woman who swims at my pool and her hair is practically white and there is not a shadow of green in it.

I wouldn't worry about it, just go with the color you like the best.  Pool chemicals do tend to keep bleaching it out, so you may have to maintain the color more often, or you may find you like the effect.