My 3 yr old twin boys were prescribed augmentin (amoxicillin and clavulanate) for what the doctor says in a sinus infection. Is it possible for them to have that at this age?

Yes. Yes, they have sinuses too. They can also get infected. Best wishes. This reminds me of a funny comic drawing of a baby as having only two glands, the giant drool gland in the head and the giant poop gland in their abdomen. Certainly by the age of three the drool gland has receded and there's enough sinus airspace to become problematic :).