So, I've recently taken the Shield spell for my character.  And my understanding is that, while you get no additional benefits from upcasting it, it does allow for it so you could potentially cast it with a level 2 or 3 slot, if, for example, you were out of level 1 slots.

However, it is not showing up on my character sheet's list of spells able to be cast with a higher slot the same way other spells do, such is chaos bolt does.  Does that mean taht Shield actually can't be upcast using a higher level slot or is it just a bug on the character sheet?

You can upcast shield using a higher level spell slot. The spell behaves the same way no matter what level spell you cast it as.

The character sheet only shows "Upcast" options for those that change mechanically. Otherwise, there would be an upward cascade where each spell level would include all spells of lower levels, which would be a nightmare.

Even if a spell does not have specific benefits to upcasting there are general benefits to upcasting: the spell becomes the higher level, which is useful if enemies try to counter or dispel it.

Quote from Memnosyne >>

The character sheet only shows "Upcast" options for those that change mechanically. Otherwise, there would be an upward cascade where each spell level would include all spells of lower levels, which would be a nightmare.

 It was already a nightmare since half of all spells do have a mechanical benefit and usually these were very good spells anyway...

But yeah, there's your answer mageman.