The problem is that you are trying to reference class methods without creating a class. 
You have three options to make this work:
1) Convert ThisAddIn to a Module. Then there won't be any issues accessing the Testing123 method as you currently have it.
2) Convert ThisAddin.Testing123 to a Shared method, i.e.:
Public Shared Sub Testing123()
Then you would access as follows:
Call ThisAddin.Testing123()
3) Create an instance of the ThisAddIn class prior to using its methods:
Dim oAddIn As New ThisAddIn
Call oAddIn.Testing123()
Update
It appears that addins are treated differently that standard classes. 
This MSDN article contains specific implementation guidance for accessing AddIn functionality from other types of solutions.
Based on this article, you need to take a couple of additional steps:
1) Create an interface to expose the functionality from your AddIn:
<ComVisible(True)> _
Public Interface IAddInUtilities
    Sub Testing123()
End Interface
2) Add a utilities class to your addin project:
<ComVisible(True)> _
<ClassInterface(ClassInterfaceType.None)> _
Public Class AddInUtilities
    Implements IAddInUtilities
    Public Sub Testing123() Implements IAddInUtilities.Testing123
        System.Windows.Forms.MessageBox.Show("It Works!")
    End Sub
End Class
3) Add the following to ThisAddIn to expose the utilities to external callers:
Private utilities As AddInUtilities
Protected Overrides Function RequestComAddInAutomationService() As Object
    If utilities Is Nothing Then
        utilities = New AddInUtilities()
    End If
    Return utilities
End Function
4) I am a little unclear on the exact syntax needed for the last step since I don't have automation installed in office, but you will need to do something along these lines:
' OutlookTest should be changed to the name of the project ThisAddIn is in
Dim addIn As Office.COMAddIn = Globals.ThisAddIn.Application.COMAddIns.Item("OutlookTest")
Dim utilities As OutlookTest.IAddInUtilities = TryCast( _
    addIn.Object, OutlookTest.IAddInUtilities)
utilities.Testing123()