I am not 100% sure. but you can try this step to get an unsecured card instead of closing the card.
As you have a secured ICICI card, apply for an Amazon pay card. This would be an unsecured card.
After receiving this close your FD-based card, now you have an unsecured card and your problems are resolved.
I would suggest increasing the FD amount and the ICICI-secured card's limit first.