Two periods at the end of the sentence isn't the only common (mistaken) usage of double punctuation.
Here are a couple other examples:
- He yelled, "Don't go!", and then he ran after her as fast as he could.
You've already got punctuation with the exclamation point, so you can leave the comma at home.
- I can't believe he didn't just ask, "Why can't you make it?".
No need for that period; the question mark does the trick.