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It's very difficult or impossible to put in a 9 Volt battery in the reverse of the right polarity.
If the fan is blowing backwards, then its motor has had a reversal of the voltage applied to it, in all likelihood. That may well be completely independent of, and coincidental to, the battery change in the remote. But, first, try unplugging the fan, and leaving it that way for an hour or more, then try controlling it again.
And check that the battery voltage in the remote is not weak, by chance.