I am not currently taking care of my girlfriend who has been sick.
What is your reason for not? Is your girlfriend relying on you to care for her?
Yes, she does but I don't have the time.
You are expected to care your sick gf. Always find time for her.
I don't love her, she has the flu and that's it. I don't care about her.
Well if you do not care about her at all then you probably should not be in a relationship with her. All you are doing is wasting both of your time, and you both deserve to be with someone you love.