"An" in Shakespeare's Taming of the Shrew

In Act 1, Scene 1, Katherine says to Bianca,

A pretty peat! It is best / Put finger in the eye, an she knew why".

I understand "Put finger in the eye" means she is fake crying for sympathy, but what does "an she knew why" mean?

I'm guessing that "an," somehow means "if," since this makes the most sense.

In Shakespeare's English, 'an' could be a clipped form of 'and', which had several meanings that have disappeared. See A Shakespeare Glossary by C. T. Onions, enlarged and revised by Robert D. Eagleson (Oxford University Press, 1986):

and, an, an'
(…)
sub. conj.

1. If; even if, though. 1H4 2.4.283: "Ah, no more of that, Hal, an thou lovest me!" (…)

This conjunction is sometimes duplicated, i.e. when Shakespeare writes "and if". See for example Caliban's words in The Tempest, Act 2, scene 2:

These be fine things, an if they be not sprites.

Returning to The Taming of the Shrew, Katherine is saying, "The best thing she can do is to make herself weep, if she knew of some excuse". (See The Taming of the Shrew, edited by G. R. Hibbard. The New Penguin Shakespeare. 1968. Page 181.)