Redness and swelling is often due to inflammation. If the nail did succeed to go into his foot, i would not doubt that it is now infected. If the area seems to be hotter than normal (feverish) this is also a sign of infection. If you do not believe it looks as if it is healing, then go to your closest emergency room or contact his physician. It is always safer to consider the more dangerous outcome just to ensure it doesn't get too bad.
Too, does he have any underlying medical conditions? Is he diabetic? Low immune system? These factors could also lead to infection as the body is not able to fight infection as well as if he was healthy. I hope you get the issue resolved and he gets proper medical attention to handle the problem. Good luck and best wishes to you both.
The problem is that oral antibiotics to not diffuse well in the lower extremities.
Unresolved redness and swelling are characteristic of infection.
It is a judgemental call, but this often ends up with a stay in the hospital on intravenous antibiotics.
Worst case is gangrene and foot amputation.
If you have any doubts, head for the ER.
My boyfriend did the something and he refused to get it looked at the top of his foot was red and swollen and walking was difficult for a good week or so... I would get it checked out to ease your mind.. just in case its infected