I'm not sure where you're getting the prompt to re-enroll. Usually it comes right after your Sims' grades arrive if you're playing them. Do they have active classes? As far as I can tell -- and I've been playing 10 households in rotation, with college students in 3 or 4 of them -- they don't re-enroll unless you're playing them. I tend to play my student Sims for a full week so as to get all their classes in.
As for the career section -- in the list you'll see the new careers that your Sims are eligible for, as well as the beginning stage of that career. For example, my Sim who was a Biology major could choose Botanist (at level 7, I think), but also Gardener, which Botanist is a part of.