Can local anaesthetic make you puffy?

Hi all,
I went to the Dr today about an infected cuticle, she ended up giving me local anaesthetic in my thumb and then she cut it open to drain the infection.
That was 6 hours ago and when she initially did it I noticed my thumb ballooned and she said that was the fluid from the anaesthetic, I’ve just changed my plaster and whilst most of the fluid or puffiness has gone down there is still one part of my thumb that is puffy – can this still be from the anaesthetic?
Can it take a while to leave the body or dissipate or whatever it does?
Does anyone know or has anyone had this experience?
She said it was Paronychia so needed draining so it wouldn’t get worse, there was no pus or anything when she drained it so I’m not sure it was the best thing to get done, to be honest!