You asked

Will my menstrual cycle be regular while I'm breastfeeding?

While you are breastfeeding, your body's oestrogen levels are low, which is why your period is either absent, or highly erratic during that time. Some women treat breastfeeding as a natural form of contraception. The trouble with that is you never know exactly when your body will decide to become fertile again. Also, you cannot rely on a skipped period to indicate conception, due to their absence during breastfeeding.
As your body's hormone production and levels normalise, your periods ought to become more cyclic and predictable. A nursing mother's first postpartum period will start at about the same time their baby starts eating solid food, or has naps longer than four hours at a time between feedings. After the first new period, you should consider yourself to be fertile again, so take precautions. Using contraception during this time is very important for mothers who have had a c-section; most doctors advise against becoming pregnant sooner than 18 months after the operation.
Barrier methods are more reliable for contraception during breastfeeding, since the progestin-only pill can change the composition of breastmilk. Using natural contraception, such as the rhythm method, can be very tricky during the shift back to regular menstruation. Try the following books for advice: Natural Child Spacing, by Sheila Kippley and Your Fertility Signals: Using Them to Achieve or Avoid Pregnancy Naturally by Merryl Winstein.

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