Can I run diagnostics on my phone on my own

There's this. I've not tested it but it's worth a try.

Test & Check for iPhone on the App Store

Hello Speedfreak001,

Unfortunately only Apple support can run a diagnostics on your phone. Give them a ring if you are having a problem with your phone by Contact - Official Apple Support

You can perform user troubleshooting from the Apple Support site, but as far as running any type of diagnostic software, no, that is not possible.