Is expiation obligatory for one who had water enter their nose or ear while bathing to cool down, and then swallowed what they felt exiting their throat and tasting in their mouth?

Water entering the nose or ear does not invalidate the fast, unless some of it reaches the mouth and the fasting person is able to expel it but deliberately swallows it. In that case, their fast is invalidated. However, if it reaches a place from which it cannot be expelled and is then swallowed, the fast is not broken. Doubt about water reaching the mouth or being swallowed does not invalidate the fast. Expiation (kaffarah) is only required for intercourse.