How to make a simple select search

Have you tried select2 ? It is easy to use and does not ruin the way in which your data is displayed, you just have to reference your select based on your ID and attach the code after your data is loaded.

Example on the web (after the page loads):

 $(document).ready(function() {
    $('#descriptionItem').select2();
 });

Applying it to your code (assuming that it is):

//Tu codigo que asigna los valores al select(creeria que lo haces con un for each)
//luego de asignar todos los valores conviertes tu select normal a un select tipo select2
$('#descriptionItem').select2();

If you need more references, you can consult them on their website.

Now, if you do not want to use any of that, I recommend you visit this thread Filter options of select box using input box value .

Greetings