AITA for showing up at my wife's workplace?

I (30F) have been married to my wife (I'll call her Eve for the sake of the post - 35F) for 9 years. She is an amazing person but her behavior the other day honestly left me speechless.

Eve got into an accident last week. Thankfully she is perfectly fine. Her car isn't though and it is currently at the mechanic for repairs. I give her a lift to work in the morning and she usually gets back home on her own.

The other day, I had a rather long day at work. I texted Eve and asked her if she wanted me to pick her up so we could go home together. She said yes. She's a doctor and works at the hospital. I got there and I texted her where I was. I waited for half an hour and there was no response other than I'll be there shortly.

I've never really been inside the hospital and she hasn't been to my workplace as well. We never discussed this there was just no need for it. Eve has always managed to keep work and home life very separate and prides herself in doing that.

Anuway our kids' sitter's time was going to be over in a short while so at least one of us needed to be home soon. I called her, texted her and still no response after half an hour. I got worried so I got into the hospital, and asked for her. They didn't just tell me so I introduced myself as her wife.

I waited inside for 15 minutes and learned that they had an emergency and she had rushed into the OR for a patient. Eve finally came and we went to my car. She asked me what I was doing and I explained the situation.

She got really angry and said she didn't really want everyone to know about her private life at work. I was really confused because from her tone, it felt like she didn't want people to know we were a couple, let alone married.

She kept pushing that if they knew her spouse was a woman she wouldn't hear the end of it from her coworkers. She said she didn't want me to be dragged in the middle of this and that her workplace was toxic at best. I may be TA here because I got mad and went on a rant about us being together for 11 godd*mn years, having two kids and that being a fact, not something to be ashamed.

The argument went on, and even after we got home, I can't bring myself to accept that she sees this as a liability. Eve tried to apologise but I still can't let this go. My friend told me she works in a ridiculously male dominated field of speciality and her concerns were valid. Was I being an AH? I feel like I am losing my mind?