I would use "sort out " if I'm trying to find a solution to a problem, or if I'm trying to clean something up or organize something. Example: It took all day to sort out this mess. "sort through" to look at things and put them in a particular order especially while searching for something. Sort through She sorted through her bag for her keys. Hope this helps!

sort through https://idioms.thefreedictionary.com/sort+through sort out https://www.thefreedictionary.com/sort+out