Looks like it could be a sinus infection, which is often caused by a respiratory disease. I would isolate this hen in a warm, clean place. Let her be for a day or so, and see what happens. If the lump goes down, then great, but if not, I would begin antibiotic treatment.
A good antibiotic for respiratory infections is Tylan50 injectable, which can usually be purchased from a livestock supply store for $15-$30. It also comes in an oral powdered form, but the injectable form works faster. The dosage is 1cc for large-fowl, .5ccs for bantams, injected into one side of the breast once daily for 5 days. Alternate the side of the breast that you inject into, and use a small gauge needle, as Tylan can make the injection area sore. Do not give probiotics or dairy products during Tylan treatment.
In case you're wondering how to inject, here are some basic instructions. More information can probably be found by searching the Internet or BYC:
- Suck up some of the antibiotic with a syringe and needle.
- Have a helper (if possible--otherwise you'll have to hold the bird yourself) hold the bird so that you can easily get to the breast.
- Find a spot on one side of the breast that looks meaty. Clear away the feathers, and swab the site with an alcohol-soaked cotton ball.
- Slowly insert the needle of the syringe into the meaty spot. Don't go too far; about 1/8-1/4 of an inch.
- Draw back the plunger of the syringe. If you see blood, relocate.
- If there is not blood, slowly but surely press down on the plunger to release the antibiotic.
- Massage the injected area for a minute or two, and then let the bird rest.
If you can't find Tylan, I would recommend trying Oxytetracycline (Terramycin, Tetroxy HCA-280, etc.). That antibiotic is weaker, but still a good choice when treating respiratory problems. The powdered Oxytetracycline dosage is 2 teaspoons per gallon of drinking water for 7-14 days. Again, don't give dairy products or probiotics during treatment. Improvement may be seen after 2-3 days, but you should treat for the entire recommended time.
Keep in mind, though, that antibiotics will only be effective against bacteria, not viruses. If this infection (or whatever it is) is caused by a virus, basically the only thing you can do is give supportive care (warmth, nutritious feed, vitamins/electrolytes, etc.) and hope that she recovers.