Ouch! It sounds like blocked ducts which you can resolve. Try to feed baby from breast as much as possible to keep the breast well drained. Also you can try massaging the affected area gently towards the nipple while feeding as well as using hot/cold packs before and after feeds. Look for any white spots on the nipple which can be a milk blister or bleb - it's when skin covers one of the openings. If possible, feed baby with the chin on the affected side or use different positions (if it's under the breast it'll be quite difficult to feed baby upside down!). Oh, you can also use something with vibration to place on the affected area too. Whenever you can, rest rest rest!!!
If you start to feel feverish, bodyaches or chills it's best to see the Doctor to get antibiotics. The antibiotics will be safe to take with breastfeeding.
I really hope you're able to clear it!! Mastitis is no fun at all!!