A garlic clove wedged against the infected area can help kill bacteria. Cashews are supposed to help dental infection. Rinsing with or applying tea tree oil, oregano oil or H2O2 (Hydrogen-Peroxid) are great Antibiotics .
You probably know that cloves can act as a numbing agent for the pain.
I suggest drinking the Lugol's. It will go where it's needed to fight the infection. Good luck.