I just wanted to add on to this because I had the same issue: enrolled a sim into university (Britechester for Comp Sci) for story purposes and then went to play in a different household. When I came back to advance the story, and have the sim switch schools to get a distinguished degree, the option was grayed out. I even cheated the four relevant skills up to 7 (when she'd been Programming 6, all others 4 or 5) and nothing. The save isn't that old, maybe 3 months; and she only had 2 more classes to go so I didn't want to drop out.
I searched the internet, and another person (I think on reddit) was having a similar-ish issue and had their sim reapply to university and unlocked the distinguished degrees. I shift-clicked to use the "skip wait time" cheat, had my sim check their application status, and FINALLY the Comp Sci at Foxbury was available! And I kept her previous class credits and GPA.
So if anyone else is experiencing a similar issue, I suggest trying Apply To University again before dropping out to reenroll.
