For medicines, you might be looking for:
* Kusuri-bako (薬箱): This literally translates to "medicine box" and refers to a traditional portable box used to store medicines.
* Iyakuhin (医薬品): This is a general term for "pharmaceuticals" or "medicinal products" in Japan. It is a broad term.
For cosmetics, you could say:
* Keshouhin (化粧品): This is the general term for "cosmetics" in Japanese.
* Keshou-bako (化粧箱): This translates to "cosmetic box" and can refer to a box for storing makeup and beauty products.
Other relevant terms:
* Setsu-to (セット): This is a common term for "set", usually a gift set of cosmetics and medicines.
If you could provide more detail about the type of box or the specific item you're interested in, I can give you a more accurate and helpful answer.