Did I violate the fourth precept?

I am a Theravada Buddhist. I got selected to a government university in my country. I got a message saying “Your online registration under Additional Intake for Special Subject for the A/Y 21/22 is available at…” When I went to the website I saw a notice regarding special intake, which is not related to me. So I thought the message I got must have been about the special intake. So, I didn’t search any further. Some time went by. Later I got to know that we could make appeals to enter a university. Then, I discovered that I had actually been selected to the university I wanted to enter. By then, the time to register had passed. As a result of confusing the message I got with the special intake, I lost the chance to register on time. I also got to know that in order to appeal to enter that university it would be better if we gave a medical reason justifying our inability to register on time. I wasn’t willing to do that because saying that I couldn’t Register due to a medical reason would be a lie violating the fourth precept. However, at the time I got selected for university and missed the chance to register, I was taking treatment for OCD and secondary depression. At the time I missed this chance, I was studying in another institute and I wasn’t mainly focusing on entering a government university. Later I sent a request to register late at the university. I was told that giving a medical reason would ensure the success of the process. In my request I mentioned that I couldn’t register initially due to a shortcoming, which from the above, was the case. To give the medical reason I said that I was taking treatment for OCD and secondary depression at this time and was less concerned about entering a university. I said that I was under treatment and believed I was in a fit state to enter, therefore I asked them to grant my request. I felt guilty that I might be violating the fourth precept by lying, but nevertheless I sent the request. It worked and I got selected to the university. My question is, considering the above facts, did I violate the fourth precept by lying? I feel guilty about it at times. I would appreciate your opinion