AITAH for asking for advice for an sexual issue in my relationship online?

About 2 weeks ago, I found out that my girlfriend had been talking to her friends about my penis size and shape, to which I asked her to explain herself. Prior to this, I have been homeschooled my whole life and had minimal socialization, so this entirely caught me off guard.
However, she told me it was completely normal and that I shouldn’t worry. I told her I didn’t think it was normal, to which she told me I could go look it up, and that it totally was. Just a bit ago I then asked about its normality on two subreddits, to which I found she was correct.
After this I went to have a conversation with her and apologize but still ask that she not share intimate details without my consent. She yelled at me and told me that I had no right to talk about our relationship to strangers online, and she wasn’t calmed down by me reminding her that it was completely anonymous.
I asked her if we expected privacy if it wasn’t even clear if we were exclusive. She told me that I shouldn’t expect her to know if she wants to be exclusive or not, and that I need to stop being so worried about her personal conversations.
She told me she was embarrassed that strangers might see our conversation. She then stormed off, and since then I’ve been getting the silent treatment, and I just need to know, am I the asshole?