You would have to check with your own areas. In the states and many others places it is not covered when a person does a willing sterilization. If you had complications with your previous pregnancies (depending on the severity of them, etc etc) it might be better for you to look into a surrogate mother to ensure your own personal health as well as the childs.
I'm in South Africa and had my sterilization done for free 7 years ago. I had complications with my first and second pregnancies,and now i'm not so sure i made a right decision because i wanna try for a girl,have two very handsome boys and they wish for a baby sister.
I guess it depends on where you live. I am in Canada, and no, it is not covered by our health plan. It is considered elective surgery. In the US, I don't believe so, but perhaps some Insurance Plans cover it? If you are in the UK, or other, I honestly don't know. You would have to check with them. Good luck.