"My younger brother is afraid of being injected."
Translation:Adikku takut disuntik.
"takut dengan" , while is also the translation from "afraid of", it is usually followed by an object/noun.
ex: - My younger brother is afraid of dogs = Adikku takut dengan anjing
Although in everyday speaking, 'dengan' is rarely used here. You could also say "Adikku takut anjing" and still be correct.