Same tube for 23mm and 28mm tires?
A tube will have a range.  Most likely the original range of that tube did not include 28.  Small tubes are usually sold as 19-23.  Yes the rubber would probably stretch to 28 without bursting but it would definitely be weak.  If you are going to spend money on new tires then spend money on new tubes.  Even same size I put new tubes in new tires.  Save the old for emergency.  Better yet save the old tires with tubes for emergency unless the tires are just plain shot.