woke up sick from a dream

So two nights ago, I had a dream where I met an online friend for the first time. Everything was going well until she said something that really pissed me off. (I don't remember what she said though). And then I just went crazy, I pushed her on the ground and I kept hitting her in the face. I just kept on going and there was blood everywhere. I remember thinking "why does it take so long for her to go unconscious?" And eventually she passed out and that's when I woke up. I felt so sick to my stomache and disgusted with myself. It's not normal to dream about things like this right?

I dreamt about the same person again last night, but this time it was such a lovely dream. Where I showed her around, went for a walk while holding hands and then we cuddled on the couch whilst watching tv shows. To me, it felt like these two dreams were related. But I'm so confused as to why I would dream about something so sickening.

The thing is, we're gonna meet each other during the summer holidays when I go to Sydney (so obviously not at my place) and now I'm actually scared. What if I do end up hurting her in some way?

I wouldn't worry too much about it. Though the dream was awful, it probably doesn't mean much and was just a really bad dream. Everyone gets nightmares from time to time.
Unless you are a very violent person and are likely to actually beat her up, I doubt you actually will. Letting this get to you will negatively affect your relationship with your friend more than anything else honestly could.

What we do in dreams does not in any way represent us in waking life.
In dreams you are disconnected from your normal memory and in an altered state of consciousness.
Dreams can also place ideas or actions into your mind without clear reason. For example you can suddenly feel enormous rage towards someone.

I have always had a lot of nightmares and they are probably the reason I get lucid dreams naturally.
Nightmares in which I hurt other people have always been the worst, but I can tell you that they have nothing to do with your personality.
They however can have something to do with new and exciting situations or your own fears.