Hey MikeW1324,
Being able to share your Health records is a great feature! In the description it shows you have iOS 15 installed. Be sure your iPhone is fully updated to software version 15.5 as keeping your software updated resolves many issues and installs important security updates. To see what you have installed, tap Settings > General > About. If an update is needed, back up your iPhone first. After updating the software, update your apps too:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Update your iPhone, iPad, or iPod touch - Apple Support
How to manually update apps on your Apple device - Apple Support
In addition to making sure you're updated, if you're trying to share with an individual they need to be in your contacts (with the correct email address listed) and use an iPhone with iOS 15 installed as shown here: Share your data in Health on iPhone - Apple Support
If you're still not able to set up sharing after ensuring you're updated and the person you're sharing with meets the requirements, we recommend reaching out to Apple Support to look into this more: Contact - Official Apple Support
Thanks for participating in Apple Support Communities.
Take care!