Unable to sign into my MacBook Air with the password I changed it too

Try this in order to reset your password

"Restart and show password reset options"

1. After entering your password up to three times, if you see the option to restart and show password reset options, click it to restart your Mac. 
2. What happens next depends on how your Mac is set up. 

• • If you're asked to select a volume to recover, select your Mac startup disk, which by default is Macintosh HD. 
  • If you're asked to sign in with your Apple ID, enter your Apple ID, then enter your Apple ID password. You might then be asked to enter the verification code sent to your other devices. 
  • If you're asked for your FileVault recovery key, enter the string of letters and numbers you received when you turned on FileVault and chose to create a recovery key instead of allowing your Apple ID to reset your password. If you lost it, follow the steps here: If you can't reset your login password.
  • If you see a message that you do not have iCloud recovery or a recovery key set up for this volume, follow the steps here: If you can't reset your login password.

1. Select a user to reset the password for, then click Next.
2. Enter your new password information, then click Next. 
3. When the password reset is completed, click Restart.

See this link for further reference

If you forgot your Mac login password - Apple Support