Send data from a form on the same page

I wonder if it is possible to send data from a form on the same page with all the code. Separately it works perfectly for me, but what I need is for the data to be sent in the same file and refreshed.

I leave my code here.

<?php 

    //Recojo datos del formulario
    $id = $_POST['intro']; 
    $dato = $_POST['datonuevo'];

    //Consulta para actualizar los datos    
    $sql1 = "UPDATE dimension_intro SET text_work='$dato' WHERE id = '$id'";

    if ($conn->query($sql1) === TRUE) {
        echo "Actualizacion realizada con exito";
    } else {
        echo "Error al actualizar: " . $conn->error;
    }

    $datosantiguos="SELECT id, text_work FROM dimension_intro ORDER BY id";//consulta datos antiguos
    $result=mysqli_query($conn, $datosantiguos);//ejecuto la consulta
?>

<select name="intro">

    <?php
    //recorro los datos antiguos
    while ($row=mysqli_fetch_array($result))
    {
        echo '<option value="'.$row["id"].'">'.$row["text_work"].'</option>';
    }
    ?>
</select>
<br>Nueva intro<br>
<input type="text" name="datonuevo"> <br>
<input type="submit" value="Actualizar" ><br> <!-- Aqui tenias mal escrito submit jaja -->
</form>

<?php
    $conn->close();
?>