persistent cough after cold seems done

Hello,

My 4.5 yr old boy has had a cough for the last 4 weeks. It began with a regular cold, but after the cold seemed ended, a dry spasmodic cough persisted for one week. He then got another cold, which is now ending after a week and a half, and the cough once again is persisting, though all other cold symptoms have gone away.

Cough is dry, spasmodic, and usually one little cough followed by two quick coughs. It sounds like he is trying to 'itch' the base of the throat to me. There is only occasionally the sound that he is expectorating anything, mostly it is just dry.

It is worse when lying down, and running can throw him into a coughing fit.
It may be slightly helped by warm drinks and sitting up and being still.

Strangely, a common pattern is for him to wake up around 3 am coughing for an hour and a half, unable to go back to sleep. Nothing seems to help except waiting it out.

He has had a history of cold virus susceptibility, of weak lungs (virus goes to his lungs quickly and hangs on).

I have not detected other symptoms to indicate allergies to pollens or grasses, but right now I am considering allergies as a possibility as we just moved to a new state and are changing from summer to fall weather (dryer, colder).

He seems to have a poor appetite right now, eats very little and slowly, and has lately complained that his stomach hurts when eating, but it is unclear as to how it is hurting.
His bowel movements seem fairly normal, although the stool appears more pale and yellowish and little softer to me right now. They occur a little more frequently than usual and he sometimes thinks he needs to go and then nothing comes. This goes along with the stomach pain he complains of, I think.

I have tried Arsenicum 30c for the cough, and thought I initially saw improvement, but now think not.

Oh yes, and for body type, he is tall and big boned for his age. He has a large round head, and is fair of skin, hair and eyes. He tends to overheat and sweat. When he gets sick, as a rule, he almost never gets a fever.

Any suggestions for this problematic and persistent cough would be most appreciated, thank you!