You are looping on lstShipping, yet looking at items from lstMsg. Is that really what you want to do? If not, change lstMsg to lstShipping as below:
Private Sub ctrSend_Click()
Dim msg As String
Dim i As Integer
Dim oItem as Variant
' Dim lstMsg As ListBox
If lstShipping.ListIndex = -1 Then
msg = "Nothing"
Else
msg = ""
For Each oItem in lstShipping.ItemsSelected
msg = msg & lstShipping.ItemData(oItem) & vbCrLf ' <--- lstShipping!
Next
End If
MsgBox "You selected: " & vbCrLf & msg, vbOKOnly, "Selected BIN"
DoCmd.Close
End Sub