Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
In the Name of Allah, the All-Merciful, the Mercy-Giving
If you did have the intention to divorce her in this way when you uttered those words in response to her request, then you are divorced. If the waiting period is over, then you may remarry her through a new nikah.
Having said this, let me advise you to learn to master your anger. If you plan to live together, you should seek marriage counseling. Unless you learn and practice the tips to control your anger, there is no guarantee that you will not repeat the same mistakes.
You need to remember that divorce is the most hated of all permissible things in the sight of Allah. So, you cannot use the words of divorce jestingly. If you do so, you are playing with the Laws of Allah which is a grave sin.
Almighty Allah knows best.
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