My son has a hard lump under his chin, which has been there for about 3 weeks now. he was put on augmentin (amoxicillin and clavulanate) for 10 days but its still yet to go away.

Time to see his doc: "hard lump" could be an abscess that needs to be incised and drained. You may need an ENT referral to get a better assessment if your primary care doctor is not sure. An ultrasound may be also required.

Not bacterial: There are other conditions in the differential diagnosis that are not related to bacterial infections and therefore would not respond to antibiotics.. For instance a sebaceous cyst would not respond to Augmentin (amoxicillin and clavulanate) and would need to be surgically excised . A calcified hematoma is another condition that would not respond.