try pulling the skin back by pulling it down to get the puss out! then use peroxide. Yes it will hurt but it will feel good! At least that what I have done in the past when I have had hang nails.
I would stop doing any and all treatments as it is probably irritating the area more. Covering the area with a bandage at all times except sleeping hours is a good idea along with frequent hand washing. If symptoms do not resolve within a few days after doing this, I would consult a doctor for a physcial exam as this might me an antibiotic specific type of bacteria that needs a prescription antibiotic
Hi there .This infected hangnail not responding to topical antibiotic, needs to be shown to a doctor immediately otherwise a paronychia may result. You might be prescribed oral antibiotic and pain killer and also may drain it or excise it under local anesthesia. Hope this helps. Take care.