Desktop project sharing an EF Code First Model with a MVC4 Web App Project Solution - entity-framework

Question

I recently added a Visual Studio 2012 Desktop Project to a Visual Studio 2012 Solution that contains several Web Apps Projects and 1 Class LIbrary Project. The Class Library handles the EF 5 Code First Database Model that is shared for all the Web App in the solution.
The class LIbrary Project is the only one I used to update the database. The rest of the web projects are just consumers of that DLL library.
Now I'm trying to add a Visual Studio 2012 Desktop Application project to the same solution. The goal is for the Desktop App to use the same Class LIbrary DLL to interact with the database.
I added the Desktop Project to the solution and created the reference to the class library DLL. After I made changes on it to access the database through this DLL, like:
ContextDB db = new ContextDB();
ClassLib.Models.Gallery gallery = (from g in db.Galleries where g.GalleryId == galleryId select g).SingleOrDefault();
After the desktop Project is built I ran it and the first error that shows is:
The model backing the 'ContextDB' context has changed since the database was created. Consider using Code First Migrations to update the database
Then I tried to solve using this line of code just before the ContextDB definition:
Database.SetInitializer<ContextDB>(null);
ContextDB db = new ContextDB();
That solved that problem but now it is showing another error related with INVALID COLUMNS in almost all the columns on the table, the error is:
Invalid column name 'EventId'.
Invalid column name 'WebsiteId'.
Invalid column name 'Slug'.....
and so on for all the columns on the table..
There's nothing wrong with the database and other projects in the solution are using the Class Library without any problem.
I'm not sure what to do now.