hello, It's good that for these complains you consulted a doctor. As per the history the child has already been given course of antibiotics and antiinflammatory medicine for the complains. Is there any history of same complaints in family?For how long the kid is having these problems? How many times the same thing happened?Is the kid allergic to anything? From when did this start to occur if it has occured before?
As it's over a month already and the kid is still not relieved, that's why giving inhaler won't cause any harm if given as per your doctor's advise.
It's safe and usually used for long duration as per the doctor's advice. But if you have doubts it's always better to talk about it to the doctor that is treating the child. Because he/she has examined the child in person and knows better about current situtaion of the kid.
Make sure you do not let the child get exposed to cold. Do not give anything that is cold to eat or avoid ice creams. Do not give anything directly to eat which is taken out from fridge, even water. Make sure the temperature is normal when the kid is eating or drinking anything.
I would suggest you talk to your doctor about it. And continue the treatment. Or a second opinion is fine if you are worried so much as the issue is related to the kid and thats absolutely fine so that you won't have any doubts while continuing the treatment for it. Hope this helped.If you have any further queries feel free to contact. stay healthy.