jQuery Mobile wraps all types of input in a div. That div holds all styles, hence, if you want to do any changes to an input, you need to apply them to that div.
To listen to changes on radio buttons, you need to use change
event.
$(document).on("pagecreate", function () {
$("#textarea").hide();
$("[name=opcmessage]").on("change", function () {
var text = $(this).closest("div").find("label").text();
$("#textarea").text(text).show();
$(".me").closest("div").removeClass("ui-icon-search").addClass("ui-icon-check");
});
});