Ex girlfriend wished me happy birthday, I told her to stop contacting me and she got mad?

bostonpilot
My girlfriend of one year broke up with me back in July. Stating she didn't want to be in a relationship because she was busy with school and her daughter etc. We had some issues prior with my father not getting along which added to the situation. She also accused me of being unfaithful which wasn't true. Bunch of red flags that I had seen leading me to believe she was the guilty one, cause I heard someone else might be in the mix. I was devestated, and kept no contact permanently. On my birthday, 8 am before my family even called, she sends a long text calling me her sunshine, wishing me all the best in the world. Her daughter, even her dog wishing me HBD lol. Xoxo blah blah. I responded ty. So the whole day that's all I could think of, and memories came back. It screwed me up. The way I took it is she wants to string me along, and I wasn't for it. So the following day I sent her a very generous email thanking her for all the good times we shared, and wishing me HBD. Said we should cease all communications, and it would be best to no longer keep contact. She wrote back an hour later saying "Nice message, believe me you will never hear from me again!!!" She sounded offended! I was expecting something like I'm sorry I hurt, I understand I'll back off. Was I right to go about the way I did? Also since that I got private calls and silence a few times last week which had never happened.
Updates
+1 y
thanks guys. After I had sent the email I felt much better after doing so, since she basically was toying with me. That's how I seen it.
Ex girlfriend wished me happy birthday, I told her to stop contacting me and she got mad?
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