Issues updating my App Store

it shows my old Apple ID which is email1@gmail.com and my new one is email2@gmail.com

So, you find your old Apple ID.

The problem is -> You can’t merge multiple Apple ID accounts.

You are sign in here .  .  .  with your Apple ID & Password.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

Check if this help you out:

For more support and assistance see -> Contact Apple for help with Apple ID account security

Contact Apple for help with Apple ID account security - Apple Support

Click here for more support and assistance.

Try signing out of the App Store/iTunes, restart, and then sign back in. Check the updates to see if the apps requiring an update are in your Purchases History. If they aren't in your Purchases History, you can delete the app, and download it using your current Apple ID if desired. You may have to restart before you can download the app again.  If the apps are in your Purchases History, contact iTunes Support. 

Purchase History Review  *

See the Apple Support articles below for contact information.   

iTunes Support – world wide   -

Apple Support schedule phone call   -       

If necessary, try Twitter

Apple on Twitter   -    

Messages chat with Apple