Actually, don't send your own ID. Answer these questions first,
1. The account you used on Infibeam, is it your account or in the name of your parent whose card you used?
2. The payment gateway has probably flagged your transaction as possible fraud. To unflag it, send the ID of the parent who the card belongs to, write a mail and state that you are their child and you used their card to order a TV at the address of your house. Also mention your parent's contact number and your contact number in case they need verification.
Also, calm down. Your parents know you have ordered so why the panic? Since you have done a transaction on Infibeam, which a reputable site, you will get your product. Payment gateways(CCAvenue) have automatic fraud detection tools in place which sometimes catches innocent orders as well. Chill out and send them a mail explaining what's happened.