Dry Cough in 5 Month Old

So my LO has this dry cough , he doesn’t do it all day just mainly when he gets upset or when he first wakes up, i dont know if he’s faking it because we give him a reaction. Sometimes it’s sounds fake and other times it’s sounds real i’m just nervous at a time like this. There’s literally no other symptoms , no fever, no mucus, nothing. He had a slight touch of pneumonia about 3 weeks ago but they gave him 2 shots for it and antibiotics and he took all of his medicine i just am confused. Is it normal? Could he possibly have allergies?