Hello kellymcmc068,
Thanks for that info and for choosing the Apple Support Communities. If I understand correctly, you are having an issue with calendar events on your iPhone, but you don't have this issue at iCloud.com. If you haven't already, please force close the Calendar app on your iPhone and restart your iPhone as iOS clears cached data and does other system optimizations when you turn your iPhone off and on.
Force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone, iPad, or iPod touch
Next, make sure your iPhone is up to date, as the updates contain stability fixes that can resolve issues like yours, as well as important security updates to keep your iPhone safe.
Update the iOS software on your iPhone, iPad, or iPod touch
Cheers!