Can I add a penance to what the priest already gave me at confession?
Doing additional penance for the sins of your life is a good thing, but we need to be careful to avoid scrupulosity. If you want to do penances over and above those assigned by a priest in confession, I recommend talking about that with your confessor. It is a good idea to submit to him your plans for additional penances and to receive his permission before you begin.
If you want to engage in serious penitential practice as a spiritual discipline, I urge you first to find a trained, experienced spiritual director and undertake this kind of penitential practice only under supervision by your spiritual director (and possibly also by your physician, if the penances could impact your health). You can read more about taking up the practice of penance in a blog post I wrote, Ready or Not, It's Lent.