Plugin program: JQuery not working in this plugin

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.