You can find cases on ebay and japanyouwant.com but they aren’t cheap. They seem popular, but I got a couple and didn’t like using them. Maybe good for storage, but I didn’t like using the tama in the case. Since the paint has already rubbed I say why bother. Get one to try if you think you’ll like it. Never know till you try it yourself. I included a link to one to help you find one.
Multiple Tamagotchi cases available. Genuine official OEM Bandai product. Includes a felt pad and sheet of stickers. CANNOT SEND TO ����������������. If there are any issues whatsoever, I'll do all I can to resolve it.
www.ebay.com
Not all are painted like the gold one you have, many are just a colored plastic. I attached a screenshot of P2s from tamashell.com. Most aren’t fully painted except for the gold and silver. I’m not sure about the two-tone red/green or black/orange.
The rest are colored plastic with just a bit of paint for the logo. Some have paint in the cracked egg area around the screen, and some have a bit of shell design paint. The shell design paint can rub off but not quite like the gold you are showing in your photo.
The only ones that have paint on the back are the gold and silver (and maybe the two-tone). Those are gonna rub off a lot.