Ok.
I think what you have is a bit complex. Consider the below... The two regex terms in the "grep{}" can be combined. I show a simple formulation without doing that. If you have just a few hundred files, tweaking this further won't make any performance difference at all. Clarity is often a lot more important than getting the nth degree of performance.

#!/usr/bin/perl
use strict;
use warnings;

print "Please enter text for string search: ";
my $search=<STDIN>;
chomp $search;

print "Please specific a directory: ";
my $directory=<STDIN>;
chomp $directory;

opendir(DIR, $directory) or 
        die "Cannot open directory: $directory \n";

my @files = grep{   m/$search\.jpg$/i 
                         or
                    m/$search\.jpeg$/i
                }readdir (DIR);

print "No files found in $directory\n" unless @files;

foreach my $file (@files)
{
   print "$directory/$file\n";
}
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Oops: if $search is a regex, you will need \Q$search\E