Adrian,
Welcome to the forums. You've got a lot going on here with this relationship. BDSM is just one of many things to consider.
First up, you've got to know yourself.
What do you want from the relationship?
Are you seeking more than a playmate?
Does being dominant in the bedroom come natural to you or do you feel like you are play acting to satisfy your partner?
How does punishing her and your fight relate?
Was she seeking for you to actually punish her for something?
Did she want you to be her "master" all the time, some of the time, or only when you were playing?
What expectations did she have for you when she asked you to take that role?
As you can see, this is all getting down to communication between your mind and your heart and then between you and your partner.
There's playing the role of a dom and actually being the dominant partner. While my T is Mr. Dom, 24/7, we don't live BDSM 24 hours a day. It's just who he is, a dominant male. Me, on the other hand, I like to switch roles depending on my mood, the situation, whatever. As you further explore BDSM, let yourself experience both sides and see if you have a preference for one or the other.
To your success,
Ruby