If so, will health insurance cover this?

you need your uterus and ovaries for hormone regulation.
You can however get your tubes "tied". I had a friend do this for the same reason at about your age. She did have some eggs removed and frozen just in case she changed her mind, which of course, she did when she met the right person. You are young and you have plenty of time to make a final decision on such an important issue. If you still feel this way at 26 or so I would say go for the tubal, but be sure to save a few eggs just in case. If you decide later on not to ever use them, some grateful woman out there will be more than happy to benefit from them!

whats that?