It is better to have an eye exam for contacts before you buy them. There are special tests that typically are not performed in routine eye exams for eyeglasses. Even you are in the good health on the regular exam, it does not mean you are the right candidate for contacts. The doctor will check whether you are irritating to the contacts and the curvature of the cornea are suitable for wearing contacts. Anyway being safe is better.
You'd better have your eyes examined and get a new prescription special for contact lenses.