There is in fact little reason to believe that this reason for celebrating the 18th of Iyar is true. The "students" of Rabbi Akiva most likely refer to those followers who fought in the Bar Kochva revolt, which lasted a full 4 years, and ended in late summer with the defeat of Beitar according to the Talmud as well as contemporary Roman historians.
The only source for the belief that his students suddenly stopped dying on the 18th is a 12th century rabbi who reported another rabbi reading so in an unknown old book. To quote the Chatam Sofer on this topic:
אמנם ידעתי כי שמעתי שעכשיו אכשיר דרי וממרחק יבואו ידרושו את ה' בע"הק
צפת ביום ל"ג בעומר בהלולא דרשב"י ז"ל ... אבל לקבוע מועד שלא נעשה בו נס
ולא הוזכר בש"ס ופוסקים בשום מקום ורמז ורמיזה רק מניעת הספד ותענית
מנהגא הוא וטעמי' גופא לא ידענא
שו״ת חתם סופר יורה דעה, רל״ג
So, "What are we celebrating on Lag B'Omer?" It seems no one really knows, but we do know that this was not originally related to Rashbi's death, as can be seen here:
https://seforimblog.com/2011/05/printing-mistake-and-mysterious-origins/