Most cases of breast engorgement will go away on it's own without any treatment.
Usually the breast engorgement will go away on it's own within 2 weeks and when the breast engorgement goes away the breast can still be full of milk although the breasts should become softer when the breast engorgement goes away.
Even though the breast engorgement goes away on it's own within a couple weeks you may still need to pump your breast to relieve the pressure on your breast.
The reason you may want to pump your breast milk after the breast engorgement goes away is to prevent infection of your breast.