If she gets mad even though you haven't done anything that might have hurt or offended her, I won't say that she is sensitive. Rather, she either has anger management issues or she just dislikes her co-employees. However, I don't think that she's being professional with handling these issues because clearly she is overtly showing her disdain. Most co-workers won't do that, as this will jeopardize not only your career but also hers.
I do think that you will always come across a co-worker who may dislike you for whatever reason. You can't please other people. And if I am in that situation, I will strive to be sensitive enough towards my co-workers, remain friendly, and communicate openly. I may try to talk to her about this because I am a firm believer that talking things over will help shed light on how to deal with the problem, or identify the problem per se. I might not be aware that I might've done something she took personally that's why she's acting all that. Or perhaps, she has a lot of worries that makes her burst with anger all the time. Perhaps, we can also agree to be civil with each other. Who know's from merely being civil, we can actually start to get along. However, if she's not open to these ideas, then I will just do my best to not let her attitude affect my performance.