BlueCreek

You'll have to ask your doctor about that specific problem, but I can tell you that not having your period does not translate into not being able to get pregnant. Plenty of people are irregular and go an extra month or two without a period but can still get pregnant. Also, it might be because your are producing milk, that's one of the main reasons women who give birth don't have periods again until after they stop breast feeding, doesn't mean they can't get pregnant again right away.

Is your medical condition why you can't try any other contraception?

Unfortunately since you are irregular, it might be hard try the rhythm method (which is really pretty risky anyway.)

The only other thing I can think of since you are irregular is to try the ovulation kit's women use to get pregnant, only instead of timing it with when you are ready, wait for a few days until after you have peaked before you try unprotected. Ask you doctor about that, probably your safest non-contraceptive option.