AITA for telling my vegetarian coworker that she was eating animal products?

I am well known at work for bringing in treats and snacks for my coworkers, everyone knows that when I being things for others they will be kept in a specific place in the kitchen with a note and I will let the shift leader know that the snacks are to share. Everyone also knows if there is no note then it is mine alone and I make sure not to store them in the kitchen to avoid confusion.

Friday afternoon I had a 3-9 shift, I came in and placed my snacks in the staff room, which is close to the kitchen. These snacks were in my bag and meant for me alone. A few hours later I went to get my snacks and found one of the packets opened. I asked around and one of my coworkers admitted to opening it, saying that they were her favourite and she thought they were for everyone.

I asked her why she ate them when she is a vegetarian, and told her that they contained animal products. She became very upset as she is apparently really serious with her vegetarianism and started yelling about how I have poisoned her with meat and yelling at me about how I brought them in even though I knew they weren't vegetarian. I snapped a bit and said that I brought them in for me and she went through my bag to get to them, and if she hadn't then there wouldn't be an issue. The rest of the shift was very tense and uncomfortable and my coworker is now refusing to speak to me and refusing to work with me, and telling people that I tried to poison her with animal products.

I've since been getting messages from my coworkers saying that I should not have brought non-vegetarian foods in and I shouldn't have said what I said as it was insensitive. I spoke to my parents and my partner and they are split. My dad and partner think that she got what she deserves for going through my stuff and taking my food but my mum and sister think I am in the wrong for how I handled it. AITA?

Edit: For clarification, the animal product was gelatin. I checked the packet at the time, and it didn't have a 'suitable for vegetarians' lable. They were haribos, and some were suitable for vegetarians. These ones were not.

Update: First of all, thank you for all of the advice given. It has been really helpful. Just a quick update. Was pulled aside by my shift leader today at work, he told me that my vegetarian coworker has been making out that it was a communal treat that she ate, as I did being in both a communal trat and snacks for myself that day, not my stuff and that is why I am getting heat from my other coworkers as I am pretty good at labeling everything non-vegitarian when I bring things in for all staff. Myself and the shift lead have been setting things straight today with other coworkers, showing recipes that I followed that confirm that it was a vegetarian safe treat, and I've made it clear that she went through my things to take my stuff. I've gotten a few apologies as they claim they didn't have the full story. Have also filled a report to the HR department to try and get ahead of everything.

Also, for the comments saying that I didn't care that she was going through my things, while I did care at the time I was more worried that a supposed vegetarian had eaten something non-vegetarian. I've got a new lockable lunch box now and intend to only use that. I've also informed everyone that due to this incident I am no longer comfortable bringing in treats, so people are pissed off at my coworker now too.

Another thing I wanted to address is my mum and sister, it isn't that they weren't pissed about the situation but that they were concerned that the way I handled the matter could be turned around and used to paint me in a bad light, which they did not want. The last thing is that one guy who DM'ed me to take the piss about how this must be a fake story because of a few spelling errors, I am literally dyslexic so screw you I guess. Still cannot believe that this happened because of a bag of fucking haribos.