Recently (within the last year) had an ovarian cyst rupture. Doctor told me I could leave and gave me codine w/ tylenol (acetaminophen). Could I be infertile?

Ovarian cyst. The rupture of an Ovarian Cyst in and of itself is not associated with infertility. It is possible that ANYONE could have fertility issues but just the rupture of a cyst does not put you at risk nor is it a sign of one being infertile.
Not . Not on the basis of the problem you've described. Even if the cyst somehow destroyed the ovary or the fallopian tube on that side (which is not likely), you should still produce eggs from the other one.