More efficient way to narrow down a range
Worksheets have a CodeName property - View Properties window (F4) and the (Name) field (the one at the top) can be used as the worksheet name. This way you can avoid Sheets("mySheet") and instead just use mySheet. This will eliminate the shtz variable, which isn't telling us anything.

Speaking of variable names, try to give them more meaningful names - it makes it easier to follow what is happening.

Like this snippet

Sheet1.Cells(counter, searchVal))


I can tell searchVal has to be an integer, but if I saw it anywhere else, I'd think it's a string.

Also with your search columns being SchCol1 - I'm sure there's a better way to do that. Maybe productColumn and such.

I have to think your series of If Not Nothing is because you were getting errors. I also have to imagine you're passing all of these values to the above code? All the columns and all the search strings?



So, the easiest way to make this more efficient is to bring it into an array. In my example, I'm returning a string instead of a range, because I assume that's what you're after. Either way, it's an example.

Option Explicit
Sub RichardU()
    Dim lastRow As Long
    Dim lastColumn As Long
    Dim searchValues As Variant
    Dim searchArray As Variant
    Dim foundRange As Range
    Dim startRange As Range

    lastRow = 10
    lastColumn = 4
    Set startRange = Sheet1.Cells(1, 1)

    searchValues = Sheet1.Range(Cells(1, 7), Cells(1, 10))
    searchArray = Sheet1.Range(startRange, Sheet1.Cells(lastRow, lastColumn))

    Set foundRange = FindInArray(searchArray, searchValues(1, 1), searchValues(1, 2), searchValues(1, 3))

End Sub

Function FindInArray(ByVal valueArray As Variant, ByVal firstString As String, ByVal secondString As String, ByVal thirdString As String) As String
    Dim rowIndex As Long
    With valueArray
        For rowIndex = LBound(valueArray) To UBound(valueArray)
            If valueArray(rowIndex, 1) = firstString And valueArray(rowIndex, 2) = secondString And valueArray(rowIndex, 3) = thirdString Then
                FindInArray = valueArray(rowIndex, 4)
                Exit Function
            End If
        Next
    End With
End Function


So what you're doing here is bringing the entire search range into an array, passing that array to your function and matching all of the search strings at once. 

You will probably have to build in some error handling. And if you want the range instead of the string, you can still bring it all into the array and return where the range would be as a pair of coordinates

Option Explicit
Sub RichardU()
    Dim lastRow As Long
    Dim lastColumn As Long
    Dim searchValues As Variant
    Dim searchArray As Variant
    Dim foundCoordinates As Variant
    Dim foundRange As Range
    Dim startRange As Range

    lastRow = 10
    lastColumn = 4
    Set startRange = Sheet1.Cells(1, 1)

    searchValues = Sheet1.Range(Cells(1, 7), Cells(1, 10))
    searchArray = Sheet1.Range(startRange, Sheet1.Cells(lastRow, lastColumn))

    foundCoordinates = FindInArray(searchArray, searchValues(1, 1), searchValues(1, 2), searchValues(1, 3))
    Set foundRange = Sheet1.Range(Cells(foundCoordinates(1) + 1), Cells(foundCoordinates(1) + 1, foundCoordinates(2) + 2))

End Sub

Function FindInArray(ByVal valueArray As Variant, ByVal firstString As String, ByVal secondString As String, ByVal thirdString As String) As Variant
    Dim rowIndex As Long
    Dim foundCoordinates() As Long
    ReDim foundCoordinates(1 To 2)
    With valueArray
        For rowIndex = LBound(valueArray) To UBound(valueArray)
            If valueArray(rowIndex, 1) = firstString And valueArray(rowIndex, 2) = secondString And valueArray(rowIndex, 3) = thirdString Then
                foundCoordinates(1) = rowIndex
                foundCoordinates(2) = 4
                FindInArray = foundCoordinates
                Exit Function
            End If
        Next
    End With
End Function


You'd just change the offsets I used to match your sheet layout.



So I was thinking about it, and I think the best way for you to simplify this would be to use a function to get the row index that matches - 

Function FindArrayRow(ByVal valueArray As Variant, ByVal searchValues As Variant) As Long
    Dim rowIndex As Long
    With valueArray
        For rowIndex = LBound(valueArray) To UBound(valueArray)
            If valueArray(rowIndex, 1) = searchValues(0) And valueArray(rowIndex, 2) = searchValues(1) And valueArray(rowIndex, 3) = searchValues(2) Then
                FindArrayRow = rowIndex
                Exit Function
            End If
        Next
    End With
End Function


You would just return the row number in the array, adjust it for wherever your array started on the sheet, and use it to get the target column that you were initially looking for.