Staphylococcal skin infection can cause furuncles (boils) and carbuncles. Carbuncles are deep abscesses extending into deeper sub-cutaneous tissues. They are common in lower neck region in staphylococcal infection. Carbuncles can be more dangerous than boils as bacteria can easily enter blood stream and affect organs like heart causing endocarditis and can even lead to sepsis.
Carbuncle near neck region should not be taken lightly as it is nearer to the spine. Proper surgical incision into deep tissues and drainage under antibiotic cover is important in your case as simple lancing and squeezing may not drain deep seated abscess properly. This cannot be done effectively in home setting. I advise you to continue the course of antibiotics (oral bactrum and bactroban cream) and visit your doctor to get the abscess surgically drained in a hospital setting.
Hope this helps. Thank you.