Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry that your pup Shadow was limping, had a nail and then his quick fall off and now has a very swollen toe.
I understand that your pup is more comfortable now, and that makes sense as he no longer has the pressure of his nail pushing on a sore toe, nor an open, sensitive quick.
But if this were just a bacterial infection he should not still have a swollen toe. And if this was only a bacterial infection as long as the toe remains swollen he should be limping. Because neither of these things happened there may be a fungal infection, there may be foreign body in his toe that seeded the infection in the first place or there may be a tumor involved.
Dogs with gray or black coats are prone to melanomas originating in the nailbed. Squamous cell carcinoma is another tumor that we see more commonly in dark coated, larger breeds like German Short Hairs originating in the nailbed.
Has he had radiographs of his foot taken to look for bone lysis (bone destruction)? If not that should be done promptly.
I also recommend aspirating his axillary lymph to look for signs of tumor cells or bacteria or fungal spores.
If he has bone lysis radiographically I would be very concerned. Given his lack of response to antibiotics exploring the site to look for a foreign body, and collecting culture samples for bacterial and fungal cultures would be the next step if you want to try to save his toe.
If this isn't one of his two center toes (which support most of his weight) I would consider amputation reasonable too.
Please let me know if you have any further questions.