What is the ruling on taking pain-relieving medication for wisdom tooth pain and rinsing the mouth with water and garlic to alleviate the pain while fasting?

Allah permits the sick person to break their fast if fasting causes them hardship, increases their illness, or delays their recovery, as Allah Almighty says: "But whoever is ill or on a journey - then an equal number of other days." So, if a toothache causes clear hardship during fasting, then breaking the fast is permissible, with the obligation of making up the missed days. There is no harm in rinsing with vinegar and salt, provided one takes care that nothing reaches the interior of the body. If it is possible to delay taking pills until night, that is better.