All of these changes are in preparation for nursing your baby. During your last trimester, your breasts might begin to leak a small amount of colostrum, which is a thick, yellow substance. Colostrum is an "early" milk that your breasts begin to produce during the last few months of pregnancy. Oct 18, - That's when a breast pump comes in handy! It lets you store milk your little one can drink later, and it signals your body to continue making milk.