After ejaculating, I can achieve a second erection but while becoming erect and for about 5 minutes after there is an aching, throbbing pain around the perineal area which then subsides slightly but mild pain does remain until I ejaculate or lose the erection.

It's causing problems between myself and my girlfriend so I'd really like to know what to do about it! Does anyone else experience this?

Go and see your doctor. Your girlfriend should be more understanding.