Hey there Bettybeekind,
Thanks for using Apple Support Communities. We understand that the Health app on your iPhone is not updating. We're happy to help.
It's a good article that you referenced with Use the Health app on your iPhone or iPod touch
Do you use an Apple Watch to sync to the Health app currently? Let's be sure that both your iPhone and Apple Watch are up-to-date:
Update your iPhone, iPad, or iPod touch
After you have updated, let's have you test for a day or so to see if the Health app updates.
Let us know if you have any questions.
All the best.