At what age is a tubal ligation possible?

Elle
I'm 18. I have severe tokophobia (fear of pregnancy/childbirth), to the extent that I'd rather die than have to go through with pregnancy. I'm absolutely sure I never want children - I wouldn't be able to handle it physically or mentally, and I don't have a single maternal bone in my body.
I don't want to use any hormonal birth control, because I've had very bad experiences with it in the past (weight gain, severe migraines, debilitating fatigue), and I don't trust any non-hormonal contraceptives. Right now, abstinence seems like the only option for me, because I'd just have so much anxiety about getting pregnant.
So, my question is, would any doctors (private or otherwise) be willing to perform permanent sterilisation on someone so young? I'm even content to wait until I'm in my early 20s, but I'm positive I want it done. There really seems to be no other option for me. Advice?