Thanks for writing to us.
It seems due to ingrowth of toenails(also known as onychocryptosis) and due to wearing ill fitted sneakers, the skin around your nail edges or the nail folds have developed infection and inflammation. To treat the same
Soak your feet twice in warm saline water
Apply an antibiotic steroid
cream over the nail folds
Take antiinflammatory painkiller like Brufen
If the swelling does not subside in two to three days or pus discharge continues, a course of oral antibiotic might be required.
Always trim your nail straight instead of cutting it in round shape. Wear open sandals or comfortable fitting shoes.
Sometimes if ingrowth is severe nail avulsion( surgical or chemical) might be required.
Hope that answers your query. Take care.