How to reinstall other apps on the App Store?

Hi kaleb127,

Welcome to the Apple Community.

Re: What apps am I able to install and update on my iPhone?

See "How to find apps" in this article (link below) from Apple Support:

How to: Get apps in the App Store on iPhone – Apple Support (AU)

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Re: How to reinstall other apps on the App Store ?

See this article for help downloading apps you have purchased before:

Redownload apps and games from Apple - Apple Support

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Troubleshooting: If needed:

If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

If you can't open the App Store or iTunes Store, buy content, or edit payment information - Apple Support

If you can’t download or update apps on your iPhone or iPad – Apple Support (AU)

All the best :-)