According to Webster's Dictionary, traditional grammar rules deem the word "who" is correct for the subject of a sentence or a clause, and the word "whom" is used for the object of a verb or preposition. The word "whom" is becoming less frequent, and it is more often seen in formal writing or when someone wants to affect a formal demeanor.
A typical example is when someone knocks on the door, the reply is "Who is it?" not "Whom is there?"
When you are dealing with "whom" and confusion about objects, it can often clarify things by changing statements into questions. After all "whom" is a question word even though it often isn't listed as such because it is going out of fashion.
Change your sentence to a question.
"Who did you make cry?"
or if you want to sound more formal:
"Whom did you make cry, I wonder?"
You are correct that the verb "to make" takes an object complement like "someone". Here, the answer to the question is the object complement. The answer could be a person's name or "Someone." In the query's example,the construction is correct, but the object complement is whom.
Change the structure of the question and you would need to change the object complement.
Did you make someone cry, I wonder?