When you created the add-on domain, it should have created it as a subdirectory under your main site: .../public_html/newdomain/. This is accessible from your originaldomain.com as originaldomain.com/newdomain/. Check to see if that's where you actually are (in your new domain, with an odd name). If so, there are some .htaccess tricks that can be done so that your newdomain.com shows up that way in a browser, instead of olddomain.com/newdomain/.

Also, how much time has elapsed since you pointed your new domain to the same nameservers that you use for your primary domain? It can take up to several days for word to propagate around the Internet Domain Name System from your registrar that your domain is now pointing somewhere else.