There is no response from native guys yet, so please let me (non native) try to answer. I don't find a grammatical mistake in your example sentence. If you would like to say more specifically, 我生活中发生的一件事情 or 昨天发生的一件事 (事情) should be more appropriate. The connotation of 事情 might be slightly more serious (or formal) than that of 事.

Whether or not the sentence is natural depends on the situation, and I think your example is also natural under certain circumustances. In my opinion, 如果可以的话 is usually followed by sentences such as 我想去美国旅游 or 我想成为世上最有钱的人. If I were you, I would just say ‘我想告诉你我生活中发生的一件事，可以吗？’

But "如果可以的话" is also understandable and without grammatical problems, and I think the listener could sense your consideration and respect. "如果可以的话" usually emphasize whether the objective situation allow you to do something or not. While "如果你不介意的话" emphasize the listener's willings, if he/she would like to listen your story or not. So,  "如果你不介意的话" is recommended in your case.