ER or no? Help!

My son has had runny nose/terrible cough since Wednesday and every time I start to think it’s getting better he dips back down into the terrible cough.

He’s 3 and I have been giving him cough medicine since Wednesday night.

He’s not running a fever but is sweating a lot and is miserable.

Is this ER worthy? I’m really worried.

EDIT: I do not have a pediatrician (or that’s who I’d be going to) due to insurance problems