Magento 2 Update cart Item price based on latest price change in custom table

I want to update the cart items using my custom API with the latest price which I am storing in a custom table.
In the first API hit it is only updating the original custom price in the item table but not updating anything else.
But when I hit the API for 2nd time it is updating the price and subtotal correctly with the custom price.

Here is my code –

        $cartItems = $cart->getAllVisibleItems();
        foreach ($cartItems as $cartItem) {
                $cartItem->setOriginalCustomPrice($my-price);
                $cartItem->setCustomPrice($my-price);
                $cartUpdated = true;
            }
        }
        $this->cartRepository->save($quote);

Please help.