dextramethorphin is a popular recreational drug and is the one in the robitussin that your cousin was seemingly addicted to. AFAIK one cannot <develop> schitzophrenia from it.
but, seeing as though he is in the institution and you are distraught i thought i would offer you words of advice from my own experience in an institution.
write him letters. he is probably lonely and wonders why everyone deserted him. they should provide care, but it might not be up to your standards. i swear that i was smarter than everyone that tried to counsel me in the hospital i was stuck in. I was only in there for 12 days, but the fact that the doors can only be opened with buttons and that everyone looks at you strangely when you go on “outings” sucks. i assume that the family put him in the institution for help and therefore he was not court ordered to be there? check it out, make sure he is attending therapy and taking advantage of what help there is there. did i mention that you should encourage family memebers should write him letters? just normal everyday stuff, not mourning him, just letting him know what ids going on in the real world. i hope he doesn’t have to stay there for really long and can be functional because even thought places like that do have television, they also have crazies. there is always someone in worse shape than your cousin. and remember that he is a person. a real human being. even though he drank cough syrup for a living. you will be in my thoughts 
how did i miss the last three threads?
maybe i provided some insight. . . sorry. . . .