password is saved on my mac air but not on my iPhone.

Verify these settings:

• Both devices have same Apple ID
• On Mac: Go to  > System Settings > [name on top] > iCloud, and verify "Passwords & Keychain" is on.
• On iPhone: Go to Settings > [name on top] > iCloud, and verify "Passwords & Keychain" is on

In addition, on your iPhone, go to Settings > Passwords > Password Options. Make sure the Autofill Passwords checkbox is on and that there is a checkmark next to "Keychain" in the "Allow Filling From" section.

Glad you got it working!