rickety/ set one's teeth

[vil]

Dear teachers,

Would you be kind enough to give me your considered opinion concerning the interpretation of the expression in bold in the following sentences?

The reason that I made the mistaken interpretation was my Bulgarian thinking so well as to put up my

Then, in the rickety bathroom, two flights down, I set my teeth and plunged into an icy tub.

rickety = dilapidated or maybe broken-down, shaky, ramshackle or ....

set ones teeth = clench one’s teeth

V.