It's in Shakespeare: Coriolanus, II,1, where it clearly means an enormous excited gathering, to greet Coriolanus after his victory over the Volscians.
.....veil'd dames
Commit the war of white and damask in
Their nicely-gawded cheeks to the wanton spoil
Of Phoebus' burning kisses: such a pother
As if that whatsoever god who leads him
Were slily crept into his human powers
And gave him graceful posture.
The etymological dictionary gives the noun - 1590s, "disturbance, commotion," of unknown origin. Meaning "mental trouble" is from 1640s; verb sense of "to fluster" is attested from 1690s.
It's not the same word as bother, though the similarity may lead to confusion in many speakers.