저는 더이상 알코올 안마셔요. is grammatically and structurally near perfect. The only nit I can pick is 더이상(더 이상) and 안마셔요(안 마셔요), just a minor word spacing thing. What people actually say is 저는 더 이상 술 안 마셔요 (술 in place of 알코올). 술 is the most common word for alcoholic drinks, spirit, liquor and all.

"I do not drink alcohol anymore" 저는 더 이상 술 안 마셔요. 난 이제(는) 술 안 마셔.

First of all, in Korean, alcohol is spelled as not "알코올" but "알콜" 알콜 doesn't mean a liquor or brew in Korean. 알콜 means only alcohol as chemical compound. Thus you have to say "저는 더이상 술을 안 마셔요" HOWEVER, there is one exception, when 알콜 means "술". If you say "alcoholism," you have to say "알콜중독" instead of "술중독"