I'm so sorry your son is suffering. Sinus infectons can be very painful and the drainage can sour the stomach so you don't feel like eating much.
No worries about the food. He will be fine as long as he is drinking fluids. You've gotten some good responses about Gatorade, popsicles, etc. 24 oz. a day is enough to keep him from being dehydrated, but more is definitely better.
The antibiotics can take a few days to kick in so you, and he, will have to be patient with it. One poster mentioned Chronic Sinus Infection, but since he's only been taking the medicine for a day and a half, there is no reason to think this will be chronic. Chronic means that you get repeated infections with very little 'well' time in between, or that you're on your 3rd or 4th round of antibiotics with no relief from the infection. (round meaning finished prescription) So no need to panic. :o)
Also, the idea of using saline nasal spray or a nedi pot is terrific. Nedi pots are an amazing, if a little disgusting, way to clear out your sinuses. You should be able to find on at Rite Aid or CVS. Basically it is a way of getting warm salted water way up your nose into your sinuses. The salty water (saline) will imediately thin the mucus and it will literally pour out of your nose. Yucky, but a great relief of pain and pressure! Your son will feel better right away and the nedi pot can be used multiple times to give temporary relief until the antibotics can really kick that infection.