Is there some rule against ending a sentence with the contraction "it's"?

It's is short for "it is'

I've ~ I have

Wasn't ~ Was not

Contractions are similar with abbreviations.

Abbreviation is a shortened form of a word or phrase. The letters forming the abbreviation are taken from the long version of the word. Here are some common abbreviations used:

Mr. - Mister

Mrs. - Mistress; feminine equivalent of Mister.

Ms. - Miss

Prof. - Professor

Rev. - Reverend

PM or p. m. - post meridiem

AM or a. m. - ante meridiem

A. D. - anno Domini

B. C. - before Christ

USD - United States Dollar

CAD - Canadian Dollar

B. A. - Bachelor of Arts

B. S. - Bachelor of Science