Take him back to the Doctor, for a follow-up.
That is what our Pediatrician says to do.. if symptoms continue or gets worse.
Just to let you know, in my city, there is a bad cold going around. ie: fevers, headache, mucus/coughing/sore throat/runny nose, lethargy, etc. My son, was out from school all last week, with this. And he is 6 years old.
Our Pediatrician, says this is going around now.
Even my Aunt has it, and she lives in a different city.
And my Mom had it too. She was out of work for 2 weeks, due to this cold. But she didn't go to the Doc right away, and hers turned into Bronchitis.
Instead of guessing, just take him back to the Doctor, for a follow up.
And yes, a child CAN get sick, again... after being sick. Or, they can also get sick again, with another virus. There are so many strains. Once my daughter was sick, got over it, then got sick again. Our Doc said that that 2nd time she got sick, it was another type of cold virus.
So it can be any scenario.
So best to take your baby, back to the Doctor.
And look out for any new symptoms or worse symptoms.
Colds typically take about 7-10 days to runs its course. BUT in infants or babies, symptoms can be different than in an adult, or it can be worse.
ie: as in things like Pertussis etc. In adults it is more mild, but in babies/young children, it can be fatal.
FYI: antibiotics are typically not used for viruses. Only for bacterial or infections. But I assume, the antibiotics were for his ear infection? And if using antibiotics, it needs to be used, for its full course as directed.
Also keep in mind, that babies cannot "say" exactly, that they have a headache or sore throat, or feel hot or dizzy or have a fever, etc. How was the sore throat, diagnosed?