Blown fuses from trailer wiring are due to either a short somewhere on the trailer wiring circuit or that the trailer is drawing too much amperage for the circuit. Since you said you installed LEDs it would seem unlikely that it's drawing too much.
Make sure that the trailer side connector are clean and free of corrosion inside and out. The main connector grounds should be attached to clean and corrosion free bare metal surfaces. The light grounds should also be attached to clean and corrosion... view full answer...