I went to Friendly Arms Inn before I went to Beregost, and when I came back by the caravan there was a little boy there who didn't wanna talk to me. I go into town and after finding Kagain I get his quest.

I'm supposed to find who I think was that boy? But when I go back to caravan he's not there, nothing happens, Kagain says nothing. I've read that after going north of Beregost and searching the caravans he will give up, but I have searched them already before while looking for an Ogre for a quest in Friendly Arms Inn.

I think I broke the quest? What do?

In the original game there's no real quest for Kagain or about the caravan, he simply says that he doesn't want to search it any more and stays with your party so you didn't break or miss anything.

I did hear this, but he doesn't say anything for me and the quest never changes.

It's enhanced edition.

But I just entered the nest few zones and Kagain suddenly dropped the voice line that he was giving up and tagging along with me.
Was very confused for a while there but looks like you were right, it's delayed.