Did Shakespeare write "A plague on both your houses."?

Not exactly. The full line is "A plague o' both your houses!" — from Romeo and Juliet, Act III.i.

Vol. 08 · Shakespeare ·Romeo and Juliet, Act III.i ·Mercutio

"A plague on both your houses."

Not quite the line.

How it's usually quoted

"A plague on both your houses."

What Shakespeare actually wrote

"A plague o' both your houses!" Mercutio — Romeo and Juliet, Act III.i

The elision "o'" for "on" is metrical. Modern quotation expands it, losing the spat, dying Mercutio's clipped venom.

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