Hello. Welcome to ask the doctor.
You seem to be suffering from Common Cold. There is no need of antibiotics in it. As this is mostly viral in origin.
Mucinex just helps in breaking the sputum, it won't help you much in cold symptoms. For that steam inhalation should be done at least 3-4 times a day as it helps the most. You should also take an anti-allergic drug like Levocetirizine.
In case you have any associated fever then you should take Paracetamol. You may continue Mucinex along with Levocetirizine.
Visit your doctor and share my opinion.
I hope it helps
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