Q:  Fell asleep on a red light, officer woke me up and had me park at a shopping center. Failed a sobriety test, and the officer ordered me a taxi. Am I charged with a dui if i was not given a citation or arrested?

A:   Looks like you should go buy a lottery ticket! If you weren't booked (fingerprinted and photographed) or tested on a breath machine, you have dodged a bullet! 
To answer your question, if you still have your license and weren't taken to the station to be processed, you were not arrested and i don't see anything being filed. 
If they took your license, then that is a different story. The fact that the cop had you drive after waking you up is very unusual....