What are the combining forms that are used with the female reproductive systems?
"Combining form" is a term used in linguistics to denote bound word forms, often Latin or Greek, that are combined with other words or word parts to form a wholly new word. "Miniskirt" (mini + skirt) and "anthropology" (anthropo- + -logy) are used in dictionaries as examples of combining forms and their function in forming new words. "Mini-" is a combining form from the Medieval Latin miniātūra. "Skirt" is a free word (not bound) from Middle English skirte. "Anthropo-" is a Greek combining form from ánthrōpos meaning "human." The second part of "anthropology" is -logy, which is a Latin combining form from -logia, which itself is from the earlier Greek combining form -logue.
You see that combining forms are very specific linguistic forms. There are only three words that are relevant to the female reproductive system that are combining words. These are estrogen, progesterone and embryo. The other relevant words (uterus, fallopian, ovary, cervix, vagina, labia, clitoris, bartholin, hormone, menstrual, ovulate, follicle, egg) generally have Latin or Greek roots that are not combining forms, though "egg" is a Middle English word with no Latin or Greek root.
"Estrogen" is formed by combining estrus + -gen (also spelled oestrus). "Estrus" is a free word borrowed from Latin oestrus; -gen is from the Greek combining form -genēs.
"Progesterone" is formed by combining Greek pro- + Latin gestare. "Pro-" is a Greek combining form meaning to be put forward or to put forth; gestare is a borrowed Latin free (not bound) word.
"Embryo" is formed by combining the "em-" variation of the Greek (borrowed into Latin) prefix "en-" meaning "in" with the Greek (borrowed into Latin) free word "bryein" meaning to swell or be full: en- + bryein.
[Etymologies from Online Etymology Dictionary.]