Yes, you have to. [Point blank.] It's because it's uncomfortable that you have to. You can't both just apologize to me and then not say anything to each other. If you do that, things will just stay awkward and uncomfortable.

You both need to address it and move on, however many or few words it takes for you to accomplish that. [See, it doesn't have to be some big long, drawn-out, overly emotional thing.]

Plus...do you really think Akamatsu-san can just pretend nothing happened and act like everything is still the same?

[She's terrible at lying, Kokichi. You know this. Terrible at it and hates doing it. A bad combination. And pretending like this never happened is pretty much a lie, isn't it?]