Are the 2015 and 2016 screens interchangeable?

If I recall correctly, yes these are largely compatible. All the parts vendors I would trust list them as interchangable. I believe there are minor differences, for example the 2015 model only includes 1 magnet for lid open/close detection so that may cause some issues. But other than that, I don't see why you wouldn't be able to use the display you already have.

Also. If you have never worked on one of these before, they require some extra care. The layout is not my favorite (that's a euphemism for it's horrible and makes me swear at Apple everytime I work on one). So I would recommend following the display replacement guide rather than going in blind.