Furthermore, I have a temper. I am fully aware of my temperament and try to control myself but I sometimes get into big arguments with my mother. I invariably feel very guilty afterwards, and sincerely repent: I continuously recite the Buddha’s name but I still feel uneasy because I fear violating the Five Rebellious Offenses. I still feel very badly about it.
One must take refuge with the Triple Jewel before taking the Precepts.
Since you are already reciting the Buddha’s name, you definitely should take refuge as soon as possible in order to receive the Buddha’s protection and guidance.
Should you decide to take Precepts, you should make sure to receive them from places that explain them and guide you on how to practice them. To take refuge and receive precepts will help you generate even more blessings that will greatly benefit your recitation.
Since you have not received the Precepts, you are not violating them when you have sexual intercourse with your girlfriend. More specifically, you can selectively receive the precepts that you can keep.
It is good that you understand that one must control one’s temper. It’s important to avoid arguing with your mother for the sake of being filial and keeping the peace in your home. However, even if you do, you are not violating the Five Rebellious Offenses, among which one may not kill one’s parents.