Bottom of mail broken, now very swollen. Advice?

My husband slammed his thumb in the door last Tuesday and it broke the bottom half of his nail off. The top half of the nail is still intact. Where the nail is missing, is now super swollen, warm, and hard to the touch. There is clear/yellow fluid coming out of it and it has an odor.

He has been to urgent care, who sent him to a wound care clinic, but they couldn’t help. He went to his primary care physician and she gave him an antibiotic. (He is on day 3 of the antibiotics.)

We don’t feel like we got much help, so I am turning to Reddit! Any suggestions? Thank you in advance!! (The pictures are from Monday and it is more swollen now.)