Swelling on jaw bone after wisdom teeth extraction

Hi - I had all four impacted wisdom teeth extracted under general anaesthesia approximately 4 weeks ago.  Since then I have had the lower left socket packed, as it was causing a lot of pain (dry socket).  I now have a 2-3cm swelling on the jawbone itself, caused by an infection as the packing did not disperse as it was supposed to.  I still have exposed bone in that socket, all of the others have healed.

I have gone back to the dentist & spoken to the hospital, and have been put on 500mg Amoxycillin for 7 days.  It's possible there is some dead bone that they may need to remove.  Will the swelling go after antibiotics/further surgery on the socket?  Will it take a few months, or will it never go?

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It's still about the same.  The Dr. said if it's still the same tomorrow, to go in and they may take x-rays & change my antibiotics, as they should be working by now.  No x-rays were taken after the extraction, or either time that I have been back since then.

I'm just worried that the swelling on the bone will stay, it is noticeable.