A tender breast lump with reddened skin often signals a plugged milk duct, especially if the lump is beneath your areola. If it is a plugged duct, you might (or might not) also notice a wedge of redness or fullness extending back from the lump toward your chest. You might also notice a little white dot on your nipple (that's a plug of dried milk in your nipple opening). With a plugged duct, the pain is pretty mild, and it comes and goes. Once the plug is out, you should feel immediate relief.
If the spot feels hot, swollen, extra painful, and you are having flu-like symptoms (achy, tired, chills), you could have mastitis (an inflammation of the breast tissue). Mastitis doesn't always involve a lump — sometimes the whole breast is painful, hot, red, and swollen. You might also have a fever (more than 101 degrees F). If left untreated, your breast can become infected.
Either way, it sounds like you have milk in your breast that needs to get out. Get it out any way you can. Feed baby on that breast as often as possible, trying to position his chin in the direction of the lump. (You might have to get creative.) Start every feeding on this breast until the problem is solved. If baby won't nurse, pump or hand express milk. You can also apply moist heat to your breast for a few minutes before feedings, and firmly massage the lump. If you have a white spot (kind of like a whitehead) on your nipple, apply moist heat and either gently pick it out with your fingernail, or have your doctor pop it with a sterile needle. (Afterwards, you may need an antibiotic ointment for a few days to prevent infection.)
Rest is crucial, especially if you have mastitis. Take medical leave from any other activities, stay in bed, and nurse like it's going out of style. If you are feeling progressively worse, your fever is rising, or you have cracked nipples (an easy entry-point for bacteria), your breast may be infected. See your doctor ASAP — she'll probably want to prescribe a round of antibiotics. Moms that start antibiotics sooner during a bout of mastitis can be less likely to wean early or to have recurrent infections.
Mastitis, a plugged duct, or engorgement occasionally progresses into a breast abscess (a ball of puss in your breast). This is pretty serious and can require surgical drainage, along with antibiotics. Avoid this by trying to catch and treat any breast problems early. If you suspect an abscess (if your lump remains tender and doesn't respond to treatment), call your doctor right away.
Of course, no website can diagnose your bump — let a doctor and/or lactation consultant have a firsthand look. (Other possible reasons for a bump in (or on) your breast: a pimple, a cyst, or a tumor.)