It is an almost absolute fact that if an American made liquor bottle is mouth-blown it pre-dates National Prohibition.
As an alternative, one can do a search of this website.
The growing strength of the Temperance movement and rising anti-alcohol fervor during the late 19th and early 20th centuries led to the passage of ever increasing restrictions on the manufacture and sale of alcoholic beverages. The power of the Temperance movement culminated in the addition of the 18th Amendment to the Constitution on January 16th, 1919; the amendment written to take effect one year after ratification, i.e., January 17th, 1920.
The famous (or infamous depending on perspective) Anti-Saloon League was primary force doggedly pursing the move towards the banning of alcohol and one of the first the successful single-interest pressure groups in the U. National Prohibition, however, was already the law of the land through Congressional passage - over a presidential veto - of the National Prohibition Act (aka the Volstead Act) on October 28th, 1919 which took effect immediately, although existing stocks could be sold through the January 16th, 1920 date.
However, there are definitive trends in shapes that mark a bottle as very likely to have been used primarily or originally as a container for high alcohol spirits intended for internal consumption, "medicinal" or otherwise.
Alcohol was of course an important ingredient in many other products also, ranging from wine, champagne, beer, and porter to most patent and proprietary medicines, bitters, and tonics to even preserved fruits.