Well done on your actions - you've followed the best course by raising with the next level of manager and by having detailed notes.
It appears that you want to have the record set right. This is a matter of fact and with your records and corroborating testimony from colleagues this should not be a problem. However, there is an implicit suggestion that you want "something done" about your current manager. In that regard, I would think carefully about what you want so that you can present it clearly and succinctly when the higher-level manager asks. For example, do you want an apology, an explanation, a transfer, a pay rise, compensation etc. It is clear that you were wronged and you feel how that is - the challenge is to avoid the desire for revenge (after all, you don't want them to know they got to you) and to focus instead with clarity on what you want as an outcome and as an entitlement. My emphasis here is on deciding what you want for yourself as an outcome and avoiding any temptation to seek to have the manager disciplined because that is for the company to decide on the basis of what they see in the case. I believe that looking to have someone disciplined can be seen as being personal, while looking for an apology, the pay rise you are due, having your record set straight is a sign of a sincere complaint without malice.
Finally, there was a previous incident, I would be inclined to include a mention of that, but not to make it the main issue, perhaps suggesting that the issue is with the error recording system and allow the senior manager to work their way to the conclusion.