MySQL Date_Format isn't working with - php

Question

I have a PHP page with a MySQL database with 2 fields that use the TIME type in MySQL. I want to convert those two fields from the 24 hour format (00:00:00) into 12 hour AM/PM format (00:00 AM) using MySQL's DATE_FORMAT('','') but it's not working.
So far, what I have done is created a 3rd and 4th field that also uses the TIME type. I send the 1st and 2nd field into the 3rd and 4th and convert the 3rd and 4th to preserve the original.
<?php
//connection statements omitted
$sql="SELECT * FROM $table ORDER BY date LIMIT $start, $amount";
$result = $mysqli->query($sql);
//Sends the original time_in data to the new format_in column.
$sql2="UPDATE $table SET format_in = time_in";
$result2=$mysqli->query($sql2);
$sql3="SELECT DATE_FORMAT(format_in,'%l:%i %p') FROM $table";
$result3=$mysqli->query($sql3);
while($row = $result->fetch_array()){
?>
//other fields omitted
<td><?php echo $row['format_in'];?></td>
//end while loop
<?php } ?>
The only thing this code does is replicates whatever was in the time_in column. Which is the standard 24 hour format 00:00:00. Basically, this code doesn't do anything. What am I doing wrong here?
EDITED to show my $result

Answer 1

while($row = $result3->fetch_array()){
instead of
while($row = $result->fetch_array()){
Based on the conversation we had in comments section:
Change
$sql="SELECT * FROM $table ORDER BY date LIMIT $start, $amount";
$result = $mysqli->query($sql);
to
$sql="SELECT field_1,field_2,field_n,DATE_FORMAT(format_in,'%l:%i %p') format_in FROM $table ORDER BY date LIMIT $start, $amount";
$result = $mysqli->query($sql);