Stringy grisle like food stuck inbetween teeth is going to require a floss, or some kind of pick to unlodge.
Waterpic with H2o2 [3% hydrogen Peroxide] will get smaller stuff that gets between teeth, and in the crevises.
Inside a cavity?? Eat smoothies, and soup. Maybe ask your dentist if you could pay it out Credit card and make minimum payments.
Waterpic might wash out the smaller pieces if set on max speed.
Other than that, you could spend half your life with a mirror and tooth pick keeping a cavity cleaned out.
Wish I could help, I got nothing.