hmm, not sure on how to change the alias, but you should definitely change your htaccess file up a bit. for a start, you don't want to route everything through the index file, such as files that actually exists on the server such as images, css files etc
Change your code to something like
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule (.*) public/index.php?rt=$1 [PT,L]
I would also consider removing the need to pass the route via $GET and instead just use $SERVER['REQUEST_URI'] instead