I'm a travel nurse, my home is in KY but I've been doing contract work all year in Texas. Do I need to file anything with KY tax since I made no money there last year?

If you are a resident of KY, you are subject to KY tax on all your income - no matter where you earned it. You will need to file a KY tax return and report your TX income.

(All states with an income tax follow this rule). 

That is correct.  When enter your w2or 1099, it will indicate what state you earned income in.