Who or whom I fell in love with?

Both are correct, but to avoid the use of ‘whom’ you could just drop that pronoun. The woman, he fell in love with, left him after a month. She is the subject. She cannot leave her/herself.

How do you use who or whom?

The Rule: Who functions as a subject, while whom functions as an object. Use who when the word is performing the action. Use whom when it is receiving the action. Kim is an athlete who enjoys distance running.

How do you use whom in a sentence?

Just be careful, because there is an exception: There is one context in which you should always use whom: after a preposition at the beginning of a sentence or clause. For example, To whom did you address that letter? (Not “to who”). And, My teacher, for whom I’m doing some research, is currently in a meeting.