JSFiddle - React, Tailwind, and code Playground

HTML

<select id="myselect">
    <option>hello</option>
    <option>world</option>
    <option>Add other...</option>
</select>

<div id="addother">
    <input type="text" id="addother_input" />
</div>

CSS

#addother {
    display:none;
}

JavaScript

$(document).ready(function() {
    $('#myselect').change(function(e) {
        if ($(this).val() == "Add other...") {
            $('#addother').show();
            
            //set the input back to an empty string
            $('#addother_input').val('');
        } else {
            $('#addother').hide();
        }
    });
});