Array is not going to help you much. The right data structure here is hash:

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

my %players;
while (<DATA>) {
    my ($team, $left, $right) = m{(.+)=(.+?) */ *(.+)};
    my @lefts  = split / *, */, $left;
    my @rights = split / *, */, $right;
    $players{$_}{left}  = $team for @lefts;
    $players{$_}{right} = $team for @rights;
}

for my $player (keys %players) {
    if (2 == grep exists $players{$player}{$_}, qw/left right/) {
        print "$player IS IN $players{$player}{right} AND",
                           " $players{$player}{left}\n";
    }
}

__DATA__
Team1=Joe / Phil , Amenda
Team2=James / Pam, Joe
Team3=Carmen , Lisa / James
Team4=Don , Phil / Carmen
Team5=Uri , Kate / Don
[download]

As you can see, it assigns each player his/her left and right team, and only lists the players with both teams assigned. It does not check, though, whether a player is not assigned more than one team on the same side.