If the domain was added correctly you should be able to access directly http://mydomain.com (your local site), yes you would not be able to access your live site then. You will have to disable the entry in the hosts file to access the live site or use http://www.mydomain.com to access the live site.
I am guessing the domain was not added correctly can you check if the domain entry was added in the hosts file. You can check the content of hosts file from Manage Domains in Enduser Panel of Ampps.