By default, we do not provide a filter for 'special_price' in Product Carousel. To check this, we would need to review the code to identify any customizations that may have been made, which would fall under our paid support services.
You can purchase support hours for this assistance.
Since you have created this module yourself, we will need to thoroughly review the code at the end and check all the functionalities you have implemented. For this, you will need to purchase an hourly package so that we can review it properly.