As a new mother, your body is still finding the balance of how much milk your baby needs. And erring on the generous side, which is a good thing.
Warm compresses before nursing are often used to increase the let-down reflex and a warm shower has the same effect, especially for a full breast.
If you can’t shower after nursing (when everything is more relaxed, literally), your breast will likely leak.
The long-term solution is patience: The leaking will get less or disappear after a few weeks or months. (There’s no fixed time frame, it varies a lot.)
For a quick fix, especially when you are not “bursting full”, you can press (not pinch!) your nipples with the palms of your flat hand, a bit like pushing towards your rib cage. This often works, at least for a few minutes. It even works during nursing, to stop the second breast from overflowing. It worked fine for me, but the effectiveness varies between women.