Question: May I take Paracetamol for a headache on Shabbos?
Answer: The Mishna (Shabbos 14:3) writes that one can’t take medicine on Shabbos. The Gemara (Shabbos 53b) explains that Chazal prohibited us to take medicine on Shabbos as doing so may lead to do such melachos as tochen, grinding. (See Tzitz Eliezer 8:15:15:4 for why this reason is still relevant).
The Mishna Berura (328:1) writes that one who is bedridden, however, or whose pain in so severe that it prevents them from functioning properly (choleh shein bo sakanah) may take painkillers (See Minchas Yitzchak 3:35:2).
R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 34:16) writes that if one suspects that their mild headache will develop into a more severe one and they will be bedridden one may take painkillers rather than wait till one is in such a state.Nonetheless, R’ Ovadia Yosef (Yalkut Yosef 4 p408) writes that Paracetamol relieves pain rather than heals. Thus one who regularly takes pills may take painkillers to relieve pain on Shabbos.