Viral respiratory infection
in kids can take about 2 weeks for complete resolution.
But some kids develop secondary bacterial infections after the virus- so after a temporary resolution, he might get sick again and in such a case antibiotics will be needed.
Just observe his activity, food intake. If they are okay, you need not worry, he will be alright soon. Since antibiotic is already started, just complete the entire course. Give him plenty of fluids.
If his activity is poor and his oral intake is poor- you might have to visit your doctor again and have some basic blood tests done like a complete blood count
Hope my answer helps you.
Wish your son a speedy recovery.