Hello aympwm,
Thanks for continuing with the issue here in the Apple Support Communities. Since the music is fine on all other devices, the only thing we can try is to erase the iPod and to set it up new using iTunes.
The first thing we want to ensure is that all your data is safe. You can make a backup in iCloud or iTunes. Use this article for help with that: How to back up your iPhone, iPad, and iPod touch.
Once you have a backup, you will need restore your iPod back to factory settings using iTunes. This option will erase all the data on your iPod. Please ensure you have your backup completed prior to doing this step. The reason we need to use iTunes to do this step is because we need iTunes to help install a fresh version of iOS to the iPod. This help article will help you to do this step: Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings. Please ensure you set the device up as new, and do not restore any information from an iCloud or iTunes backup yet.
Once the iPod is set up as new, you will need to re-download a couple of songs to test if you can search. I recommend starting with iTunes purchased songs first. You can re-download these when you sign in to the iTunes Store from the purchased tab. This article will help: Download your past purchases. If the issue is no longer happening, try restoring a couple of songs that your imported from other sources. If the issue is only occurring with those songs imported from other sources, there is an issue with those songs.
If this issue is no longer happening, we know the issue was with some data on the device or in the iOS version, which will most likely be saved in your backups. You can manually bring data back using iCloud or iTunes, but do not restore from the backup as you will bring the problem right back in. Depending on whether you have a Mac or PC and the iTunes version you have, you can use one of these 4 help articles will assist you in getting your music and other data back to your iPod from iTunes:
1. iTunes 11 for Mac: Connect or disconnect your iPod, iPhone, or iPad
2. iTunes 11 for Windows: Set up syncing for iPod, iPhone, or iPad
3. iTunes 12 for Mac: Sync iPod, iPhone, or iPad
4. iTunes 12 for Windows: Sync iPod, iPhone, or iPad
If the issue is still occurring, you may want to have the iPod checked at an Apple Authorized Service Provider or Apple Retail Store. They can check the iPod hardware. Use this link to find a service provider in your area: Apple find locations.
Thanks again and have a great rest of your day.