What is the ruling on going back on an oath sworn by a female relative of mine not to give my son a certain medicine, after I found benefit in giving him the medicine?

A Muslim should not swear excessively. It is recommended to fulfill a Muslim's oath to their brother, unless there is a benefit in not doing so, or a harm in fulfilling it. If your relative swore an oath upon you to refrain from giving medicine to your son, then if her oath was in the sense of a request or a clear oath, fulfilling her oath is recommended. You are not required to offer expiation (kaffarah) if you do not fulfill her oath, but she is required to offer expiation if it was a clear oath. If the medicine is beneficial and your son needs it, there is no harm upon you in not fulfilling her oath. However, if something else can serve the same purpose, then it is preferable to fulfill her oath. The expiation is binding upon the one who swears the oath, not upon the one to whom the oath is sworn.