I bet that there is a short on the new tail light. That popped the fuse and probably the blinker relay. As for the tail light I would not use it again without getting a new one. You probably would be able to get a replacement for free if its a reputable company at all.
To get parts I like to use Partzilla. Here is a link to the relay https://www.partzilla.com/product/ho...b28c4765c6a71c