storage automation

If I understood you correctly, try placing this together in your Worksheet_Change event codes, right at the top.

Private Sub Worksheet_Change(ByVal Target As Range)
    Dim f As Range, s As String, a As String, i As Long, j As Long, placed As Boolean, alerts As Boolean
    
    'set to false to disable MsgBoxes
    alerts = True
    
    If Target.Count = 1 And Target.Value <> "" Then
        If Not Intersect(Target, Range("BB2")) Is Nothing Then
            s = Target.Value
            placed = False
            Set f = Range("B:R").Find(s, lookat:=xlWhole) 'find for scanned code within columns B:R
            If Not f Is Nothing Then
                a = f.Address
                If f.Offset(1).Value >= 15 Then 'full, find next
                    Do
                        Set f = Range("B:R").Find(s, after:=f, lookat:=xlWhole)
                        If Not f Is Nothing Then
                            If f.Offset(1).Value < 15 Then 'not full, add 1
                                placed = True
                                f.Offset(1).Value = f.Offset(1).Value + 1
                                If alerts Then MsgBox "[ " & s & " ] stored at cell [ " & f.Address(0, 0) & " ]", vbInformation Or vbOKOnly
                            End If
                        End If
                    Loop While a <> f.Address
                    If Not placed Then GoTo fNext 'no empty storage left, find next avail space
                Else 'not full, add 1
                    placed = True
                    f.Offset(1).Value = f.Offset(1).Value + 1
                    If alerts Then MsgBox "[ " & s & " ] stored at cell [ " & f.Address(0, 0) & " ]", vbInformation Or vbOKOnly
                End If
            Else 'none found, add to next avail space
fNext:
                For i = 2 To 20 Step 2 'rows loop
                    For j = 2 To 18 'columns B:R
                        If Cells(i, j).Value = "" Then
                            placed = True
                            Cells(i, j).Value = s
                            Cells(i + 1, j).Value = 1
                            If alerts Then MsgBox "[ " & s & " ] stored at cell [ " & Cells(i, j).Address(0, 0) & " ]", vbInformation Or vbOKOnly
                        End If
                        If placed Then Exit For
                    Next
                    If placed Then Exit For
                Next
                If alerts And Not placed Then MsgBox "No more available storage!", vbCritical Or vbOKOnly
            End If
            
            Range("BB2").Select
            If placed Then Target.Value = ""
        End If
    End If


    ...
    ... your existing codes here
    ...

End Sub

The cell the code is reading is BB2. You have to unprotect your sheet and unlock this cell first, since it's locked and protect in your file. You can edit it to be another cell you like.
The idea is to have this as the "input textbox", so have this cell selected, then scan your codes. It will be searched for a match, and sees the number of pallets below it, adds 1 OR find another match or for a next empty cell if it's already 15. I've added explanatory comments to help you understand the codes.