I was wondering what might cause a feeling of discomfort that feels like you just ate an overly-large meal, but has lasted for a week now.

Bloating.: The symptom you describe would be called "bloating" and can have many causes within the GI tract. I would be very concerned if you haven't had a bowel movement in this week as that could be consistent with an obstruction which might require urgent intervention. Otherwise, you would need some testing - blood tests, abdominal ultrasound and CT scan at least.