At the very least, when you caulk the outside/top of the window, if not using any of the other methods such as remove casing/inject low expansion foam, add flashing, etc, then at least protect from water ingress with more than a bead of caulk: try to use an actual fillet -- a triangle shaped fill of caulk that will direct and shed any water that runs down the wall to the window.
For inside, you can temporarily prevent passage of air, especially if you can't get it stopped with better methods outside, by using anything that stops air passage: rolled up cloth, tape, clay, etc. By which I'm considering temporary measures that make the room livable TODAY! but should be removable without making any mess of the wall or woodwork/window frame.
It would be better to use an integrated approach as outlined above, considering fixes starting around the window within the wall, then both outside and inside as appropriate. But I've seen situations that need a temporary fix NOW, and can be remediated correctly over time...just hope you can get to a 'best' solution.