Clomid is technically safe for you to take while breastfeeding, however, it may seriously decrease your supply.
As for conceiving while breastfeeding...if you're prolactin level is too high, that may interfere with ovulation, and then when ovulation starts to occur, it may cause the lining you develop to be too thin to support the pregnancy. I think it may also interfere with progesterone. Thus, you can have prolactin checked, but since there is no precise perfect number, doctors want you to wean to give you the best chances of conceiving. Probably partly for their success rates, but also because it's somewhat pointless to go to all that effort when the body isn't prepared. It's such a tough place to be.
As for conceiving while breastfeeding...if you're prolactin level is too high, that may interfere with ovulation, and then when ovulation starts to occur, it may cause the lining you develop to be too thin to support the pregnancy. I think it may also interfere with progesterone. Thus, you can have prolactin checked, but since there is no precise perfect number, doctors want you to wean to give you the best chances of conceiving. Probably partly for their success rates, but also because it's somewhat pointless to go to all that effort when the body isn't prepared. It's such a tough place to be.
