When trouble-shooting something like this and trying to isolate a problem, it's important to only change one thing at a time.
In this case, starting from "everything working properly"...
- Add one of the extra wires, then check to see if it works correctly.
- Install the lights back into the lens and check it again. (perhaps something is getting compressed when they're installed in the lens and that creates the short?)
- I suggest then removing the first wire, etc., (go back to "everything works" state).
- Add the wire to the other side, check, mount in the lens, check again.
- If that side also works correctly, reinstall the first wire and check both sides together.
At some point in all of that, the fuse might blow again, but hopefully you'll have more of a clue what caused it because you only changed one thing.
Another random thing to check... make sure that the screws and connectors you used aren't creating a short circuit by touching another area of the metal part.
Also make sure you're using a fuse of the correct amperage.