The biggest problem is that redo is outside a loop. There is nothing to redo. Maybe this is what you mean to do (with print commands added for tracking process) :

my @n = (10..100);
my $i;
my $j;

LINE1: for ($i; $i < 10; $i++) {
   $i = $n[int rand @n];
   $j += $i;
   if ( ((5500 - $j) < 10) || ((5500 - $j) > 100) ) {
      print qq{Inside "if" condition $j\n};
      redo LINE1; 
   }
   print $j,"\n"; 
}