The OP appears to not know what he/she is allowed to deliver as an air exception driver. Air exception drivers can only deliver items that have a 1, 2, or 3 on the label as opposed to the blacked out square. Delivering anything with the blacked out square is a ground package, delivering ground entitles you to ground wages.
The OP needs to speak to his/her shop steward and the steward needs to pressure UPS to hang a FT bid in the building where this is occurring. The OP is clearly doing the work of a FT driver and that position needs to be filled.