Awwwwww

That sound will break your heart! It sounds like both you and the vet are right. I think that there can be a happy medium, where she gets lots of attention, and a little alone time. Maybe a special toy or a kong will help her entertain herself. Something she ONLY gets at alone time? I sort of hovered over mine for a bit, but I would put them in the gated kitchen or in their pen in the bedroom when I needed to do stuff and couldn't watch them. It's just like a baby, if you give in when they cry, they will be whiners

If you must go get her, wait until she STOPS crying and is quiet, that way you don't reward the crying.
Good luck, I know it's hard