How popular is a select according to the previous select taking data from the database?

Question

So guys, I’m trying to create two selects being that one carries the specialties of doctors recorded on a table at the bench and the other shows the doctors according to each specialty marked, i am already managing to put the data of the specialties in the first select as you can see here:

  <div class="form-group col-md-6 ">
                                
    <label>Especialidades</label>
    <select name="Especialidades_idEsp" id="Especialidades_idEsp" class="form-control"  required>
      <option value="">Escolha a Especialidade</option>
          <?php
                                        
                                                      $result_esp = "SELECT * FROM  especialidades ORDER BY nome_especialidade";
                                                      $resultado_esp = mysqli_query($conexao, $result_esp);
                                                      while($row_esp = mysqli_fetch_assoc($resultado_esp)){
                                                        echo '<option value="'.$row_esp['idEsp'].'">'.$row_esp['nome_especialidade'].'</option>';
                                                      }
                                                      
                                        ?>
                                      </select> 
                                    </div>

this is my connection to the database:`<? php

$severname = "localhost"; $database = "clinicalsys"; $username = "root"; $password = "root"; //now the connection is created below $connection = mysqli_connect($severname, $username, $password, $database); if (mysqli_connect_errno()) { echo "Failed to connect to Mysql: " . mysqli_connect_error(); } ?>`

here is my file that takes the data of the names of the doctors of the database and compares with the specialty :

<?php 

    include 'conexao.php' ;

$Especialidades_idEsp = $_REQUEST['Especialidades_idEsp'];

$result_med = "SELECT * FROM medico WHERE Especialidades_idEsp=$idEsp ORDER BY nome";
$resultado_med = mysqli_query($conexao, $result_med);

while ($row_med = mysqli_fetch_assoc($resultado_med) ) {
    $medicos_post[] = array(
        'idMedico'  => $row_med['idMedico'],
        'nome' => utf8_encode($row_med['nome']),
    );
}

echo(json_encode($medicos_post));

?>

this is my javascript script to try to show in the other select the name of the doctors

<script type="text/javascript">
    $(function(){
        $('#Especialidades_idEsp').change(function(){
            if( $(this).val() ) {
                $('#idMedico').hide();
                $('.carregando').show();
                $.getJSON('post_medicos.php?search=',{Especialidades_idEsp: $(this).val(), ajax: 'true'}, function(j){
                    var options = '<option value="">Escolha o Médico</option>'; 
                    for (var i = 0; i < j.length; i++) {
                        options += '<option value="' + j[i].idMedico + '">' + j[i].medicos_post + '</option>';
                    }   
                    $('#idMedico').html(options).show();
                    $('.carregando').hide();
                });
            } else {
                $('#idMedico').html('<option value="">– Escolha o Medico –</option>');
            }
        });
    });
    </script>

and finally the second select:

<div class="form-group col-md-6 ">
                                        <label>Médicos</label>
                                        <span class="carregando">Aguarde, Carregando..</span>
                                        <select name="idMedico" id="idMedico "class="form-control" required>
                                        
                                        
                                      </select> 
                                    </div>

I know it got big but someone could help me ? I can’t fix it