Although nothing prevents you from reconfessing, it’s not necessary at all, and the priest may eventually get annoyed and talk to you about scrupulosit. You can be confident that you are forgiven for all current and past sins when you have made a sincere confession and the Priest has absolved you. He represents Christ, after all - and he does so no matter how he does it.
We all often think we weren’t specific or descriptive enough, but the truth is, you could confess only to what commandment you broke. It’s up to the Priest to decide if he needs more information in order to absolve you or to help you deal with the sin in future.
Confession is mystical and we must be sincere, although confession out of fear of hell is also good enough for forgiveness. But it’s not some kind of magical incantation where everything has to be done just so according to a set ritual. That would be more akin to magic, and that itself could be considered a Sin. So, go to confession and then leave joyfully.
You might also want to read up on St. Faustina’s personal revelations about the Divine Mercy. I believe this was Jesus reminding modern man about God’s mercy. You know, St. Faustina is a recent revelation, but even the Confession as we know it today had to start sometime, and that was more than a 1000 years after Christ (I don’t remember the exact year off the top of my head).