If you need to read the values that the user entered in a text box before the record is committed to filter the possible values for the second text box then first you should set the autopostback property of the AxBoundField to true. Also you need to set the UpdateonPostback property of the AXForm.

UpdateonPostback property is set if the record cursor needs to be updated when post back happens, so that other controls could read the change. You could then use the row.GetFieldValue("FieldName") to get the value that that user entered in the text box.