When I change my password for Apple login it changes it but when I try to use it, it doesn't work.

Did you sign in here with it? If so it works. What message do you get when it doesn't work?

If you signed in with a different Apple ID, see

Change your Apple ID (Be very aware of the restrictions here.) https://support.apple.com/en-us/HT202667

Before changing your Apple ID using a computer, sign out of all Apple  services that use your Apple ID. If you are going to use an iPhone, iPad, or iPod, then stay signed in with your Apple ID on only that device. This instruction is taken from the above document under the heading Before you change your Apple ID.

For sign out purposes, see Where can I use my Apple ID? https://support.apple.com/en-us/HT202659 “This list is provided for informational purposes only and is subject to change without notice. It's not intended to include every feature or service that uses Apple ID. Visit the Apple ID support page for more information.”

There may be some redundancy, but see What to do after you change your Apple ID or password 

 https://support.apple.com/en-us/HT204071

If you have changed your ID or password, have you followed the steps in this article?

What to do after you change your Apple ID or password - Apple Support.