https://www.antique-bottles.info/medicine-chests/

I think what you have is an antique apothecary chest !! Look above the bottles at the link above and scroll down to see several variations !! I am not sure that the symbols were original to the chest except for the leaves at the top
and sides !! By it having the leaves I would think it may have been as herbalists chest !! Cant see the symbols well enough to tell !! Its possibly from the turn of the century, 1900 to about 1930 just from what I can see !! Value would depend on its condition !!
These came in many configurations depending on what the user needed !! Some had places for medicine bottles and others did not !!