Disagreement or Conflicts Between Sisters

I recently experienced a disagreement through a message on a social network called Facebook. It was someone that I knew in my personal life in which we called each other sisters. This how the conversation began:
Me: Hello funny acting person lol
Her: Hello, no
Me: Yes, but anyways how are you doing?
Her: Acting funny
Me: Exactly
Her: Hey Casa! You ok now, but you was tripping last night
Me: Hey! I'm good and how was I tripping last night because I said you were funny acting
Her: Yes because that's not true
Me: Why that's not true
Her: Because how I am being funny with you and what reason would I have to be acting funny with you None what so ever
Me: So that is when I told her how I felt and how I don't get attached to people too quick, but I really do like her as a sister, but we don't talk like we use to and I know that she be busy with the kids, church, and her husband, but a text or phone call wouldn't hurt sometimes. It's like she had distant herself from me and I didn't know why.
Her: She told me how she felt and then said well you are going to have to get over that feeling because it is not like that at all.
Me: Oh, trust me I will get over it.
Her: You are making a big deal out of nothing and she is sorry if I feel that way and she hate that I am offended about her response.
Me: I'm not making a big deal out of it I just see it as expressing how I feel. Why you say that I'm offended by your response
Her: Because you said oh trust me I will get over it
Me: You said I need to get over that feeling so that's why I said oh trust me I will get over it
Her: Ok
Me: I'm about to leave it along and I don't want you to have a bad day or be in bad mood
Her: Ok
Me: K, well hopefully you will have a better day
Her: Ok
The End

I felt like I did make a compromise when I said that I would let it be and I told her to have a better day. The two strategies that I have learned about that might help to manage or resolve the conflict more productively would be to be carefully about the choice of words I choose to use and to stop being in my feelings so much. These strategies might be effective because it can stop me from having another disagreement over petite stuff as people would see it. I feel as though our disagreement was deeper than that because later on I found out that she was not only doing me like that, but other closer friends as well.

To my colleagues, I would like you all input and advice regarding my disagreement. How have you all learned to be more effective communicators as it relates to conflict resolution skills?