The code you posted has an extra End If line, but that aside it does act on unread items in the Inbox. The burning question relates to my_Sub, which you haven't shared. It seems likely that any issues relating to the processing should be found there.
Option Explicit

Public Sub Unread_Emails()
Dim myNameSpace As Outlook.NameSpace
Dim myInbox As Outlook.Folder
Dim myItem As MailItem
Dim lngCount As Long
    Set myNameSpace = Application.GetNamespace("MAPI")
    Set myInbox = myNameSpace.GetDefaultFolder(olFolderInbox)


    MsgBox myInbox.UnReadItemCount
    If myInbox.UnReadItemCount > 0 Then
        For lngCount = myInbox.Items.Count To 1 Step -1
            If TypeName(myInbox.Items(lngCount)) = "MailItem" Then
                If myInbox.Items(lngCount).UnRead = True Then
                    Set myItem = myInbox.Items(lngCount)
                    Debug.Print myItem.Subject
                    'Call my_Sub
                End If
            End If
            DoEvents
        Next lngCount
    End If
    Set myNameSpace = Nothing
    Set myInbox = Nothing
    Set myItem = Nothing
End Sub