Can an unmarried woman, who is not sexually active, use the contraceptive pill for a medical purpose?

Yes. When the contraceptive pill (the birth control pill) is taken by a woman who is not sexually active, the pill does not deprive sexual acts of the procreative meaning, because there are no sexual acts. Therefore, the moral object is not evil, and the act is not intrinsically evil. When an act is not intrinsically evil, the morality of the act then depends on the other two fonts of morality, intention and circumstances. So if the intention is good, and if the good consequences of taking the pill outweigh the bad consequences, then the act is moral.