How to become an administrator for SQL Server
Since you have made sure that you have SQL Server installed on your machine all is left is to make sure that you follow the following steps to create a database. 

1) Go to Server Explorer right click Data Connections and Select Create New Sql Server Database...



2) This will open a pop-up window enter your MachineName\SQLEXPRESS in Server Name section or select a server name from the Drop down list. 

3) Enter the New Database Name.. . 



And you are good to go.