Your use of a global filehandle 'FH' inside a loop isn't a great idea. If the open fails then the nested while loop will use the already open handle FH which was left open to whatever file was opened last. Also since you've taken the trouble to define $dir why not use it when you open the file?
open (my $fh,'<',"$dir/$filename") or die " ... $!";
Another thing to watch out for is the directories '.' and '..'. Your code will pass these into $filename and attempt to open them. Use the file test -d $filename to skip directories. Or use -T $filename to find text files and ignore everything else.
A final suggestion is to use indentation inside loops and control blocks to help you keep track of the open and close curly braces.