For this issue, you can log in to your Airtel account, go to Your Profile, change the email address and save it. Now, you haven't informed us, whether you have the same phone number registered for the 4G hotspot. This is important because all the transactions or whatever interactions you do, those would be registered with the phone number you have with the telecom service you are availing. In other words, your phone number is your ID for every telecom service. If that is the same, then other aspects can be changed with much more ease.
So, you can start trying with the Airtel App on your phone, there you can see your balance too. This app is for finding everything under one umbrella.
You can also log in to the Airtel site and make the change. If that too doesn't work, you use the customer care feature and make them call you. That way, it is more likely for them to take prompt actions.