I have weak core muscles as well due to bad posture.

I think if you (or myself) were to suddenly sit upright all day long, yes it would hurt because were not used to it. Maybe put a stick on your desk or somewhere on your computer screen, phone wherever that says sit up. And every time you notice it just try to straighten for a little while. I've done this (without the sticky, just sitting up as I remember) and usually it only takes a minute or so before I slouch back to normal.