Will God punish me by not letting me enter the college I desire, because I vowed to Him not to return to insults, then broke my vow? And what should I do for Him to bestow His forgiveness upon me?

This is a supplication against oneself, that one should not enter college if one returns to cursing. If this happens, repentance is obligatory, and this act must be abandoned. "The one who repents from sin is like one who has no sin." So, if you repent, it is hoped that you will be honored with what you aspire to. If he had said, "I pledge to Allah to abandon cursing," and then broke his pledge, he must offer expiation for breaking an oath, in addition to sincere repentance, because cursing is not the characteristic of a believer. The Prophet, peace and blessings be upon him, said: "Cursing a Muslim is فسوق (disobedience/impiety), and fighting him is disbelief."