When I add drop shadow to a still image, it crops the image

I don't have enough info about your project structure and if there are any other effects applied

to your image ... but, you can try to nest your image with all the effects applied without the drop shadow,

then apply only the drop shadow to the nested one ...

you can also try to drag the drop shadow effect in the effect controls panel above or below the other effects,

sometimes the structure of effects makes a big difference, premiere reads them in order ...