Stop Duplicated rows

1) Add an "error check" column that is basically a concatenation of your address fields.... =A1 & " " & B1
Anytime an item is added to your database, make sure that cells gets filled in, too. Let's say that column is C.

2) Do an IF test at the start of your SUBMIT routine. Something like:

 If WorksheetFunction.Countif(Range("C:C"),TextBox1.Value & " " & TextBox2.Value) > 0 Then
   MsgBox "Address exists in database already"
   Exit Sub
End If

....the rest of the macro code

Another option: Use the Find method to see if the Street Name exists and whether or not the house number is different.

Basic Code:

Private Sub CommandButton1_Click()

    Dim strStreet As String, Msg As String
    Dim rFound As Range, rRng As Range
    Dim lrow As Long, lHousenum As Long


    lrow = Sheet1.Cells(Rows.Count, "B").End(xlUp).Row
    lHousenum = Me.TextBox1.Value
    Set rRng = Sheet1.Range("B2:B" & lrow) 'where to search for the value
    strStreet = Me.TextBox2.Text

    Msg = "The house number and street already exists - duplicate entries not permitted."

    Set rFound = rRng.Find(strStreet, LookIn:=xlValues)
    If Not rFound Is Nothing Then
        Select Case rFound.Offset(0, -1).Value
            Case Is = lHousenum
                MsgBox (Msg), vbExclamation
                Me.TextBox1.Value = vbNullString
                Me.TextBox2.Value = vbNullString
            Case Else
                'code to write to sheet
        End Select
    End If

End Sub

That won't find all the matches. If the address to search for is 123 Main St and the first 123 it finds is 123 Lemon Lane, it would mark that as not a match, when in fact 123 Main St may exist elsewhere.