I’ve found a good makeshift sharps container: an old liquid laundry detergent bottle with a piece of tape on it marked “BIOHAZARD: SHARPS.” It meets the local requirements, isn’t going to end up with me or anyone else getting jabbed, and is simple and cheap.
Honestly, you should check your local and state regulations. Medical waste needs to be disposed of properly, and what is considered properly depends on where you are. I happen to live in the boonies, and it might as well be medieval Europe as far as anyone cares. Most hospitals and fire departments can help you dispose of medical waste appropriately if you ask for help 