I'm not on birth control but my dr said every month a cyst will rupture on one of my ovaries. Does this cause infertility? Or is it normally ok?

This is normal. The cyst that develops is what allows the egg to move to the outer edge of the ovary and be released to enter the fallopian tube. The cyst is only a problem if it becomes big enough to cause pain and does not rupture or the fluid released when it does rupture irritates the lining of your abdomen, called the peritoneum.
Monthly Cysts. Your doctor was describing the normal process of ovulation. Each month the woman has a menstrual cycle whic is really all about getting pregnant. Ovulation is when the cyst containing an egg ruptures and releases the egg to the fallopian tube. If the egg is fertilized and you become pregnant then you do not have a bleed otherwise in about 2wks the body sheds the lining and starts over.