You now have to deploy your web application/web service. I assume that your files are on the local file system. In that case you can do it manually. To do it manually you can go to IIS (Control Panel -> Administrative Tools) and set up a new virtual directory. You can put the files under the wwwroot folder or just point to the current location of the files on your file system. Once that is done you will be able to access it locally through localhost (e.g. http://localhost/pushWS/Service.asmx). You will also be able to use your ip address instead of localhost. You have control over the url. I just put pushWS because that is what you had earlier. When you name your virtual directory you can call it anything you want. And since your ip address is public you should be able to test it. I'm willing to test it from my browser once you're set up.

Now if you run your application from visual studio by pressing F5 you will always get the development server (e.g. localhost:3307 or whatever number it decides to use). That's normal. If you want to run through IIS it easier to go through the web browser (you must set the virtual directory before you can access it in the browser directly). If you need to debug you can attach the debugger to the aspnet_wp.exe.