Hey, it happens! It even happens to girls, but I don't think it hurts quite as bad for us to hit our woohoo as it does for you fellas to hit your dingaling.
If it makes you feel any better at all, I've been riding for over 25 years and I've recently (in the last few years) caught a saddle horn to the nether regions when a horse did something I wasn't prepared for.
I, too, believe that she was just likely trying to lighten the mood after it happened in an attempt to get you to relax. She may have taken it a bit far and made you uncomfortable but I'm sure that was not her intention. I've found that when I do something silly to make other folks laugh, if I laugh with them and poke a bit of fun at myself, they tend to forget about it faster. If you act like it really bothered you for them to laugh, then they're more likely to hang on to it and bring it up again and again.
Don't feel embarrassed about it, it's part of learning how to ride. You'll get bruised in places that have never been bruised and sore in muscles you didn't even know you had. Take it as a learning experience so that you can learn how to avoid it next time.
I can only venture a guess on whether tighty-whities are really so much better, but I assume they must be something special to male riders because all the cowboys I know wear them instead of boxers.