Apple wants me to update my payment information but when I press continue nothing happens

Change, add, or remove Apple ID payment methods - Apple Support

Try updating it through appleid.apple.com and see if that fixes it for you.

madisonrae2017 Said:

"Update: Apple wants me to update my payment information in my settings but when i go in and press continue nothing happens"

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A Phishing Scam, Perhaps?:

Is this an eMail?: Apple is NOT going to send you an email upfront about your payment info. So, if this is an eMail that told you all of this, then without a doubt, it is a phishing scam --- and you, so it seems, fell for it. :(

So, Modify your Credentials: --- ASAP

Do So Here: Apple ID - Official Apple Support

1. Open: and use a new eMail account
2. Assign: a never-before-user password
3. Modify: your method(s) for payment
4. Change: your security questions and sewers
5. Forward: this eMail to: reportphishing@apple.com

Use this Link: Avoid phishing emails, fake 'virus' - Apple Support