국 corresponds to following hanjas: 國, 菊, 局, 鞠, 鞫, 麴, 匊, 掬, 跼, 麯
Moreover 국 is a native word for 'soup'. As you can see, 국 has a ton of meanings, and country (國) is only one of them.
The one used in 약국 is '局' and, according to wiktionary, it means 'office', 'shop' or 'department'. Makes sense to me.