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I'd not call it necessarily normal or always the case, no. But, it can & does happen indeed. It is almost certainly the beginning of a either lymph node (absorbing swelling), or possibly a beginning abscess.
Preferably the first, the lymph node, as that may come and go; and the abscess can be a bit more involved.
But the extraction, will tend to make the swollen area subside, irregardless of it being a lymph node or an abscess. I hope this adds clarification for you.
*PS: If you have any further concern, please don't hesitate -OK?
Sir, how is the swollen area doing? Hopefully no pain!