Is it obligatory to re-perform the prayers that I combined and shortened at the university campus, knowing that the distance between it and my hometown is a distance that permits shortening, and that shortening becomes permissible after leaving the city limits?

What you did, shortening the prayer in your city of residence before traveling, is an error according to the majority of scholars. The correct ruling is that shortening the prayer is not permissible except after leaving the city and passing beyond its houses. They based this on the Almighty's saying: "And when you travel throughout the land, there is no blame upon you for shortening the prayer," and on the action of the Prophet (peace be upon him), who prayed Dhuhr in Medina with four rak'ahs and Asr in Dhul-Hulayfah with two rak'ahs.

Those prayers of yours are invalid, and you are obliged to make them up, according to the generality of scholars, based on the Prophet's (peace be upon him) saying: "Allah's debt is more deserving of being fulfilled." While Shaykh al-Islam Ibn Taymiyyah holds the view that you are not obliged to make them up because you were ignorant of the ruling. Although this opinion has merit, the view of the majority is more preferable and safer for absolving oneself with certainty.

Therefore, you must ascertain the number of prayers you performed in this manner and make them up until certainty or a strong presumption of absolution is achieved.