My Son had that EXACT SAME THING.
But his meds, helped.
He even had the Conjunctivitis. For which he had antibiotic eye drops.
The Conjunctivitis is basically the Croup, but in the eye. And is common.
Take your son back to the Doctor.
With Croup, the airways/throat can get constricted. That is why he was prescribed the corticosteroids.
But it cannot be taken for long.
Steroids, only helps with the inflammation/constriction of the airways. It does not cure the illness if it still there.
Watch for secondary infection.
And any change in symptoms.
Young children cannot spit out mucus very well nor effectively.
Hence they keep coughing... due to the Post-Nasal dripping down their throat... this is then a gag reflex, and they cough. As the mucus drips down.
Also watch for coughing from the chest.
Coughing... originates from either:
1) the sinus/post-nasal dripping, or
2) the chest.
3) or both.