The answer depends on whether you were charged and either tried and convicted or plead guilty to the possession offense. Based on what you have stated, that "two days after being arrested" you were allowed to leave Texas, it sounds as though matters never progressed beyond the arrest. Certainly, you were not on probation unless you were convicted or plead guilty. Probation is something done under court order following a conviction or plea. If you were under probation, you would know about it.
Based on these facts and assuming their accuracy, it seems that you did not lie on your application. A mere arrest is not a conviction. It should be noted, however, that depending on the institution, some applications require that you divulge whether you have been arrested in the past. If the question was about an arrest and not merely a conviction, then the failure to disclose your arrest may represent a more serious omission.
Nonetheless, if the application is as you describe it, and your school has based its decision to hold your account on the application, then your school's actions are suspect. Large institutions can be difficult to deal with and rather bureaucratic. I recommend you contact an attorney who has experience in education law or in dealing with universities. The Illinois Bar Association should be able to help in that regard. Good luck.
What did the application ask? If it asked for arrests, you would have to answer yes. If it asked for convictions, based on the few facts set forth in your question, you would be able to answer no. you should check with the courthouse back in Texas to backup your vague memory.
Your situation involves important and complicated matters of law and fact. I urge you to consult with a lawyer on this matter.