I've been told that xem can be used in place of thấy - to see and also nhìn - to look at. Is this true?
That is kinda true. Xem is very commonly used in North Vietnamese instead of thay or nhin but in general (in the case of seeing) thay is referring to suddenly seeing something and indicates a very short timed action while nhin and xem would last longer.
Echoing @schbranigdo: When do you use xem instead of thấy or nhìn or coi?
So, in this sentence, "xem" means "see", but in a previous sentence, I translated "thấy" to "watch" and it was marked wrong (the word they wanted was "see"). So, I'm kind of confused about the "see/watch" words.
Contextually this sentence has none . it seems to only make english sense as "you look for my pair of shoes"