The size, shape and color indicate a homeopathic pharmacy bottle. If you can decipher the monogram, you might be able to check online Syracuse, NY city directories.
The original firm, Clinton Pharmaceutical Co., was founded in Clinton, N.Y., in 1887 by William McLaren Bristol, Sr., and John R. Myers. It was incorporated as Bristol-Myers Company in 1900 and by then had moved from Clinton to Syracuse and then to Brooklyn. The company first made drugs for physicians, but after World War I it concentrated on the laxative Sal Hepatica and other over-the-counter...