I'm annoyed at my gf's stress/sadness
How does her stress/sadness annoy you?
Her stress is causing me to be more stressed.
If your girlfriend is stressed out, it falls on you to help her out of it. That is what you do when you are in a relationship, it comes with the territory.
I thought we aren't suppose to worry, empathize or care about each other. We are all self reliant individuals who are only in relationships for sex and money.
Well this makes sense why you feel that way then. A solid relationship calls for you to be there to help her when she feels stressed. Try not to allow her stress to stress you out, but instead look at it as an opportunity to make her feel better.