Installing SQL Developer makes no difference here, it is a java application. You need to install Instant Client and you'll need to download and unzip the sqlplus, sdk and basic zips. You then set LD_LIBRARY_PATH to point to the dir you unzipped those packages in and export LD_LIBRARY_PATH.

Occassionally Oracle distribute instant client with a symbolic link missing and that stops DBD::Oracle building. If this is the case look in the unzip dir for a lib called something like libclntsh.so.12.1 and create a symbolic link from libclntsh.so to libclntsh.so.12.1 if it does not already exist.