Brief Answer:
Enlargement and pain suggests infection or abscess

Detailed Answer:
Hi.
Thanks for your query for your Father- male 73 years- couple of lumps behind the ear - head and neck very painful - getting bigger in spite of - under treatment with prescribed antibiotics

May I please know a few more details for me to understand the problem and give probable solution:
Since how many days are the lumps and started the antibiotics ?
Any history of fever, chills, any medical problems like diabetes ?
What is the size of lumps and whether the pain in neck and head on the same side ?
Is he given only the antibiotics or also given anti-inflammatory medicines like Ibuprofen ?

I would suggest the following in such a patient with similar history.
-Give anti-inflammatory medicines like Ibuprofen or Diclofenac for reducing the swelling and pain.
-Get the blood, urine checked for routine, infection, sugar and as required on clinical / physical examination of the lumps, neck and in general.
-To see whether the pain in the neck and head is due to the enlarging lumps or is altogether a different problem...
-Get a Consultation of an ENT or General Surgeon for more accurate clinical examination, investigations, ultrasonography / FNAC / incision and drainage if pus has already formed, to change over to more appropriate antibiotics and other symptomatic and supportive medicines.

It looks that the lumps whether the lymph nodes or sebaceous cysts have got infected and hence the increase in size and pain in the neck and head, which can be referred or involvement of the muscles.

Once the problem is getting settled , more accurate investigations to get a diagnosis as what these lumps are can be done. Let the acute problem get settled first.

I hope this answer helps you to get an early diagnosis , proper treatment and best possible cure for the said problems. Please feel free to ask for more if you need to or if you feel if there is a gap-of-communication.
Wishing you a very happy and healthy new year...

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