As Zaxo says, using SQL::Statement, or a parsing module of some kind may be easier, but I think your problem could be solved simply using another 'inner' read...something like this (untested!).

while (my $line = <SCHEMA>) {
  if ($line =~/create table \".+?\"\.(.+?)$/mos) {
    $table_nm = $1; 
    print BIGLIST "$1 \n";
    my $keep = 0;
    while ($line = <SCHEMA> && $line ne ')') {
       $table_hash{$table_nm} = 1 if ($line =~ /$var_of_interest/);
    }
  }
}
[download]

Cheers,
Ben.