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If it is recurrent even after antibiotics for one month than go for certain investigations like cbc and pus culture.Start complete course of proper antibiotic accordingly.
Swollen earlobe might be due to spread of infection locally.
Also give him nsaid to subside pain,redness.
Most likely it is due to suppurative otitis media
In chronic cases with effusions, insertion of tympanostomy tube
(also called a "grommet") into the eardrum reduces recurrence rates and tympanoplasty
is also required after complete cessation of discharge.
Consult your ent specialist
for further guidance and proper medical management.