Hope...My son went through what sounds like something very similar for years. He is now six, on singulair daily but otherwise healthy as on OX. He was in the 0-10/% weight for years too and is now 90%. I will spare you the details because you are living it...but the same main 'cough' issue that went on for '3'+ years (9mo.-4yr+). We did it all GI Specialist (Berrium/XRAY), Allergist, Pulminologis/CHOP and eventually a 'NOSE/EAR/Throat CHOP...who answered our prayers.
Here was the ultimate diagnosis/cause for us, which may not be the case for your son as I am not a doctor...BUT, he did in fact have reflux while he was young which if doesn't come up/out mouth can go back down and into either the lungs, ears, throat, chest...causing different symptoms for different children. For us, chronic cough..ear infections, sinus infections. We would/could clear one set of symptoms but not all (mainly the persistent cough). He was on prilosec until age '3' along with 'Flovent' low dose steroid (avoid if possible)which did help some but not enough. At age, 5 (and a mommy on anti-depressants due to lack of sleep) we went to see the Nose, Ear, Throat (CHOP) who checked our sons 'Adnoids' which were in fact extremely swollen. He did in fact put him on long-term singulair (for possible indoor/outdoor allergies), removed his 'Adnoid's, put in a 2nd set of tubes in ears (just in case) and our son has been healthy since. (Almost '2' years). He gets sick like all kids but is no longer coughing every night and sick 3 weeks out of 4 each month. Bottom line: Anything (reflux, asthma or allergies) can inflame your child's assophogus (I think that's the correct term) causing a chronic cough,especially when lying down. Initially the reflux, then swollen 'Adnoid's' and nasal drip(drip back down throat-not out nose, rarely had signs of outward nose stuff) caused his cough. Removal of cause, can hopefully remove the cough. SO...you have to find the cause. Not easy but worth it. Hang in there. Call me if you want and I'll give you the name's of any specialists, particularly the nose/ear/throat guy. Best of luck.
C. Bates ###-###-####