Why did Nano explode?
Nichijou's characters frequently have over-the-top reactions, this is just another one of those.

Here's a clip from later on that demonstrates my point (out of many) - http://m.youtube.com/watch?v=UD95EI3zD8A (no plot spoilers, but don't watch it you want to watch everything chronologically)

Nano's explosion was a purely a manifestation of her fretting and embarrassment, She wasn't actually hurt too badly and appears uninjured in the next scene.