Looking for and searching for is both translated as "keresni" to Hungarian. However, if you are searching for a doctor, you are opening every door and drawer to actively, phisically locate the doctor. :) The translation assumed it is not the case and you are simply asking around for a doctor.
Regardless, both should be accepted. Searching for is equally as correct and the inconsistency with which "looking for" and "searching for" are accepted and rejected here is eternally frustrating. I can't remember how many I've reported now.