A peer of yours is edgy towards you, and you are pretty confident that you have not done anything intentional to cause it. She is clearly agitated when you interact, despite your attempts to be cooperative and open.
Often an uncalled-for behavior is more about that person, than it is about you. Remember that.
Also remember that it is inappropriate, likely uncalled for, and quite unprofessional, but we ALL work with others that occasionally behave in a less-than-desired manner. Not everyone can be as self-managed and smooth as you 🙂
At the same time, what to do?
The first one is more uncomfortable, but usually the best. Have a non-threatening dialog about the situation and how to remedy it together. In this case, someone behaving in a negative tone is often a result of something deeper. You have threatened her authority in some way, you have said something that was taken wrong, or perhaps issues outside of your view are affecting her perception of you. You will need to find out through some discovery with her. At the heart of it, yes, she has some level of insecurity but you cannot affect that other than external reassurance.
So, initiate a time to discuss with her how you can better work together. Putting it that way takes a little of the threat out of it. Use the word “I” more than “you.” State how you are perceiving the relationship, especially if it has taken a nosedive lately. See that you articulate your desire to collaborate better with her so that you both can be more productive. It is not an easy talk, but you will find that keeping a level head during it and pushing through positively will pay off.
The way I put it – “The best thing to do is often the most difficult thing to do.”
Then we have your second option. If this is indeed a result of her own insecurities, just let her work through it and keep yourself sane. Focus only on your behavior not being negatively reactive to something she is doing. Remain true to yourself, and remain focused and productive on everything else despite her behavior.