Is this sentence correct or even make sense, I'm trying to put this in my essay.

"The pain I felt when I would see him cry sickens me."

There is the verb 'felt,' which is past and the verb 'sickens,' which is present tense.
Im very confused right now,help!
Of course you may have verbs of different tenses in the same sentence (I ate breakfast yesterday, and I'm going to eat breakfast tomorrow, too)-- but each tense refers to the time of the action of its verb. So if you were sickened at the time of the pain, use 'sickened', but if you were sickened at the time of the writing of the sentence, use 'sickens'.

However, you have another problem in your sentence: the 'would' of past practice should appear in the main clause (within the subject), not the subordinate clause. It should read:

The pain I would feel when I saw him cry sickens/sickened me.