Firstly I’d suggest wrapping your JS like this:
(function ($) {
$(document).ready(function(){
$("#Yes").click(function(){
$(".apptype").show();
$(".specify").hide();
});
$("#No").click(function(){
$(".specify").show();
$(".apptype").hide();
});
});
})(jQuery);
You’re also enqueuing jQuery twice, and the above the above script twice…. and with your shortcode you don’t need to declare the DOCTYPE, or wrap your from in an HTML tag.
I would also include the bootstrap CSS file in the HEAD of document.