My son's age is showing as 13, but he is 14.

Click on the link to read how to 'Update the birth date associated with your Apple ID' - Update the birth date associated with your Apple ID - Apple Support

- "Be sure to enter your correct date of birth. After you change it to any age below 13, you can't edit it."

For a child under 13 (or in a country where your offspring is considered to be a child) you will have to contact Apple:

Click here --> Choose your country or region - Official Apple Support Select your country, then a product and work your way down the menu until you reach the help you need. If you do not find it, select a different topic and work you way down to any option that results in a telephone or chat request.

Contact Apple for support and service - "See a list of Apple phone numbers around the world." - Contact Apple for support and service - Apple Support

I have never needed to do this but from reading the document no email is involved. I believe in most countries you can do this when an account is considered not to be a "child" account, i.e., over 12. In that case no special permissions should be required.

Also, is Apple trying to send you a notification by some other means? Do you have notifications turned on for your account?

If it's a problem with you receiving emails then many reasons for that could well be outside anything Apple can help you with. Junk mail filters or other filtering services that Apple has nothing to do with, etc. However, it wouldn't hurt to call them if this is something you cannot resolve on your own.

Review: About your Apple ID email addresses - Apple Support

Did you check your junk mail?

Did Apple provide a solution?