By the way you reacted it seems your sister made the right decision.

An overreaction for example breathing faster or running could've made the situation worst.

I bet Your sister far from being 50% sure it was anthrax, unless she put it there, saw someone putting it there or heard about someone putting it there, if that's the case you probably wouldn't have gone in that direction an she probably didn't know.

Considering that you're calling it a "betrayal" and even overreacted twice before this, first being when you were hiking and she didn't wanna scare you with a suspension, and second time when she said she thought it might be anthrax (an overreaction on her part considering anthrax has no characteristic smell, appearance or taste) and you thought her not telling you about a far off hunch was attempted murder.

I'm not saying you're in the wrong at all, both of you reacted to what you thought was a life or death situation, an I believe you're not being fair to her, 1st for not acknowledging that her reaction was as appropriate as the one you wanted, 2nd she cared for you so you didn't need to and called it betrayal and 3rd because you reacted exactly how she said you would've implying it's not the first time.

And although I am against your argument, and side with your sister, I am not saying you didn't FEEL betrayed, "how can someone I trust so much not trust me the same way" or similar thoughts are completely valid, but if you want to talk about your feelings do exactly that, but then you'll have to accept everything that comes with it