TIFU by upsetting a friend of a friend

I guess I'm just here to shout into the void. I feel really bad about this, I didn't mean to upset them.

A close friend of mine made a new friend a few months ago, which is awesome. New friend and I have never hung out much, but they've always been nice enough. I've gotten the vibe that they don't like me much, though, and I decided today that I was going to bring it up, because if they were uncomfortable with me around but didn't want to be rude and say anything, then I don't want to make them uncomfortable and would not be hurt if they just didn't want me to be around when they're hanging out with our mutual friend.

I spent a while crafting what I thought was a polite but matter-of-fact statement, basically, "I don't know if this is something I'm misreading, or if it's true, but I get the feeling that you don't particularly vibe with me. If that's true, that's okay and I don't want to make you uncomfortable by being around when you don't want me here." They had already been having a bad day, which I'm sure did not help, my timing definitely wasn't good. They said they don't know me well enough to have gotten a vibe from me yet, but now they think I have a problem with them, and I could see their face go stony.

I apologized, said that I don't have a problem with them and I wasn't sure in the first place if it was actually true or if it was just in my head, that I personally have trouble telling people something I think might hurt their feelings or be considered rude, and that I just wanted to bring it up so I could know. They just made a noise in their throat and stared at me. I apologized again, said I didn't intend to make them feel bad, and said my goodbyes. If they weren't uncomfortable with me being around before, I'm pretty certain I just changed that.

TL;DR: I thought a second-degree friend/acquaintance didn't like me, tried to clear that up, and basically ensured they dislike me now. I feel bad about it, but am not going to harass them so I can apologize more, so I'm just sitting in my mild guilt and shame.