If I'm following you, I would fashion a data structure like this:

%protein = (
    protein1 => 'ASFGTHTRHTHRHTHTRHTRHTR',
    protein2 => 'ERYRYTRYHTRHTGEFEWWFEEFFFFREFRGRE',
    #...
);
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Then it's just a matter of looping over the file, looking for an existing key, and running length. Similar to this:

use strict;
use warnings;
use Data::Dumper;

my %protein = ();
my $key = '';
foreach my $line (<DATA>) {
    chomp($line);
    
    # Get the key if it's a key line then skip to the next line
    if ($line =~ /^>protein/) {
       $key = $line;
       next;  
    }
    
    if ($key and $line) {   # So this is the protein 
        if (exists($protein{$key})) {  # Have we seen it before
            # Test the length and assign if greater
            $protein{$key} = $line if ( length($protein{$key}) < lengt
+h($line) );
        } else {
            # We haven't seen it before so just assign
            $protein{$key} = $line;
        }
        $key = '';  # Reset Key
    }
}
print Dumper \%protein

__DATA__
>protein1
ASFGTHTRHTHRHTHTRHTRHTR
>protein2
ERYRYTRYHTRHTGEFEWWFEEFFFFREFRGRE
>protein3
AWEERERGRGRGREGRGREGRRRRRRRRTTHTHTRHRHTRHTR
>protein2
AASEFEFEFE
>protein4
REYTRHTRGRVEVCREVR
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