Do you think I should tell my friend about her coworker hitting on me?
Why do you want to tell you friend about this?
She was like: "You're lying, he does not like you and I heard him talking behind your back".
If your friend might get upset about being told this maybe you shouldn't bring it up. This could also show that your friend has some sort of insecurity when it comes to this situation in particular and it would be good of you to be sensitive to that fact.
Who cares if she's having a hard time?
If she's having a hard time and feeling insecure, you should care simply because she IS your friend. She shouldn't have accused you of lying, but you being rude to her won't help. This may be a situation that should just be dropped.