In my own personal opinion at 18 both you and your girlfriend are way too young to even consider a permanent form of birth control. You have your whole lives ahead of you! What's the rush to sterilize yourselves?! Why not just use condoms or the pill for several years before taking this drastic measure?
At 19 I was in a long-term relationship and we also said that we didn't want kids. We even talked about one of us getting an operation to guarantee we wouldn't get pregnant. Well the realtionship didn't work out and I'm now 25 (26 in August) and due to be married in Setempber to a wonderful man. We both want children and look forward them so much.
What I'm saying is most of the time what we want at 18 or 19 isn't the same as what we come to want at 25 or 30. What if one of you gets the op done and then 5 or 10 years down the line you decide you want kids? Trust me it happens all the time.
As far as the whole health issue thing goes...well show me a family that doesn't have health problems! My family has arthritis, cancer and health disease but that's not going to scare me out of having children.
All I'm saying is that you and your girlfriend should really think about this. Use condoms and the pill together for at least a couple years and see how your attitudes change.
Take care and best of luck to both of you!
Nic