Is it true that we’re not supposed to confess on Rosh Hashanah itself? If so, what a person do when they feel pain over their aveiros on Rosh Hashanah and they feel a strong urge to confess to Hashem and express their deep remorse? Should they hold it inside and focus on Hashem’s kingship, since that is the focus of the day? Does Hashem judge kindly when a person feels remorse but holds it inside? Confessing would soothe my own conscience, that’s the reason I would feel the urge to confess. That’s a selfish reason and I should probably listen to what Hashem wants and hold it inside until after Rosh Hashanah ends? Maybe it brings atonement when the pain of not confessing when the urge to confess is strong?
As you write, Rosh Hashana is not the time to confess, even though you want to. We are not to confess our sins, because right now we are being judged and therefore right not it is not appropriate to do so, even though we might want to. The theme of the day is thinking that H-shem is our king, and that we are subjecting ourselves to His will. This is a form of doing teshuva, because all aveiros are because to a certain degree we were missing in our recognition that H-shem is the supreme king over us and that whole world. Therefore the form of teshuva on Rosh Hashana is by returning to the basics of everything, and the starting point of Judaism- that H-shem is the king over everything. Confessing sins and the other parts of teshuva will be done during the other 8 days of Aseres Yimei Teshuva.
Have a Kesiva V’chasima Tova