Do you need antibiotics for this?

This is a furuncle near the arm pit caused by previous abrasion of the skin and became infected by scratching.
Most cases would flare up into an abscess and pus formation and would need surgery for incision and drainage. If the doctor would not give oral antibiotics, it would take days for it to  mature into a  full blown abscess; usually 7days. If the doctor would give anti-staphylococcus antibiotics, it will turn into an abscess in 3 days time; less pain and less time to endure it. But I encounter patients who had been misinformed about taking antibiotics and taking medicine in general.  They thought taking herbal supplements could help. Naaaah.
Cold compress would help ease the pain and reddening of the area.  But the abscess will continue its course. You still would need to see a doctor for it and take antibiotics.