JSFiddle - React, Tailwind, and code Playground

HTML

School: <select name="school" id="schoolContainer">
    <option value="None" selected>None</option>
    <option value="DeSoto">DeSoto</option>
    <option value="Hillsboro">Hillsboro</option>
    <option value="Grandview">Grandview</option>
    <option value="Festus">Festus</option>
    <option value="R-7">R-7</option>
    <option value="Home-Schooled">Home-Schooled</option>
    <option value="Other School">Other School</option>
</select>
    
    <input type="text" id="newSchool"/>
    <input type="button" id="otherschool" value="Insert"/>

JavaScript

$(document).ready(function() {

    $('#newSchool').hide();

    $("#schoolContainer").change(function() {
        var val = $(this).val();
        
        if (val == 'Other School') {
            $('#newSchool').show();
        } else {
            $('#newSchool').hide();
        }
    }).change();

});