Very quick answer : don't 'forge' variable name. Use an array. If you realy need to 'forge' name, use an hash:

my %names;
$names{$linename.$counter} = "use pricedb;" ;
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With an array:

#my $line1 = "use pricedb;";

my @lines = (
    "use pricedb;"  ,
    "..."           ,
    "..."           ,
);

for my $counter (1 .. 10) {
    my $rowsaffected = $dbh ->do($lines[$counter]);
#...
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Better, without $counter:

for my $line (@lines) {
    my $rowsaffected = $dbh ->do($line);
#...
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