There is no being accepted or being rejected. Your sims will always get accepted. But not every sim gets a chance of obtaining a distinguished degree (which I see has happened to you).
So for now, you could wait some time (about a week or 5 days) until you can apply again hoping to get your sim into distinguished degrees. Be sure to build up skills during that time!
Or you could take up a regular degree (arts and humanitarian at Foxbury, science and other stuff at Britechester). It won't benefit you as much as distinguished would (start career at level 7 if possible and less entry pay), but if your sim graduates with honors (GPA A+), the benefits will be the same as distinguished without honors.
