Should I get a vasectomy?

Im 22 and my wife and i have been discussing me getting a vasectomy. We just had our first child. We really do not want another child. Pregnancy was extremely difficult for my wife. She was violently ill for the entire pregnancy and after about 5 months it became physically painful for her. She had an emergency c-section 5 weeks early because she was developing hypertension and the baby had stopped developing. Because of her size and makeup her doctor told us that another pregnancy would be just as bad or worse and possibly more dangerous. She cannot take birth control because it makes her sick, she has tried many different types and they all have the same affect. Her doctor strongly recomends not using any other type of birth control other than condoms because they might be dangerous for her. We do not use condoms because we can only use one brand due to allergic reaction to the condoms and the brand we can use are extremely uncomfortable for me and destroy the experience.