I don’t recommend this word. We call that a MEDICAL KIT: https://books.google.com/ngrams/graph?content=medicine+case%2C+medical+kit%2C+first-aid+kit&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Cmedicine%20case%3B%2Cc0%3B.t1%3B%2Cmedical%20kit%3B%2Cc0%3B.t1%3B%2Cfirst%20-%20aid%20kit%3B%2Cc0