This would probably be the WORST time to drop feedings or stop breastfeeding. It is very important to continually empty the affected breast to prevent serious complications, like infection or a breast abscess. Also remember that this is TEMPORARY. We know it stinks, but breastfeeding will be enjoyable again soon.
Take measures (like these) to heal your breast, and prevent future bouts of mastitis by managing engorgement, feeding baby frequently, pumping when you are away from baby during feeding times, avoiding tight clothing or accessories that put pressure on your breasts, getting enough rest, and doing your best to keep your immune system going strong.
If you have a history of frequent mastitis, blood or pus in your milk, your fever is rising, your nipples are cracked, or you are feeling sicker by the hour, talk to your doc about starting antibiotics ASAP. (These are signs that you have an infection.)