It is hard to remember this kanji by its origin because it changed too much. However, I will think of a way to help you remember it.
医 looks like a 矢 in a container. 矢 means “arrow”.
This container is used for store alcohol. When someone got shot by the arrow, the doctor using the alcohol to reduce pain.
So 医 stands for “doctor”.
Note: Below is the origin and development of the kanji 矢.