Engorgement happens in the initial transition phase between colostrum and milk production as your breasts get used to making milk. What youre describing sounds like recurring mastitis and the conventional wisdom of nursing and pumping frequently with antibiotics for the infection can indeed lead to rebound infections. Mastitis is caused by increased milk production that is not being emptied effectively from the breast. Now here is the catch, when we pump a lot to keep it reallllly empty, the stimulation if too much, can increase production and the process may begin again. A good solution may be to only feed on one breast every few hours but completely emptying it then alternate breasts between feedings. Cabbage leaves, verrry cold may help decrease your milk supply but be careful you can decrease it to gone that way. Please feel free to call for a consult, you don't say if you have seen a lactation professional but I would be happy to help.
K. @ The Nestingplace