Hi.
Abusive behavior doesn't just mean outright hitting, kicking, or slapping; it can also include shoving and verbal threats, including breaking up with you or threatening to break up with you in order to control your behavior. I'm glad you are following your instincts. Your boyfriend's behavior raises more than a red flag.
People who think the abuse is their fault may keep the abuse secret from friends and family. But this is not your fault. Clearly, your boyfriend will need to get help in order to control his impulses. If you've only been dating a short while you may not be invested enough to wait for him to change. In fact, it can be dangerous to wait it out in an abusive relationship, since the behavior often escalates into more extreme violence. I encourage you to think about ending it with him soon.
Before breaking it off, though, it might be helpful to plan ahead. Share your troubles with your friends and family members and tell them what you plan to do. Ask them for their support and companionship during this transition and ask them to look out for you.
If you decide to break up with him, do it in your home or in a public place that affords an adequate amount of privacy for a conversation, but where you are not completely alone with him. Ask a friend or relative to be close by (maybe in another room) when you talk to him. Try not to be alone in public in the period following the break-up. Avoid isolated areas at school or work. Ask a friend or relative to accompany you out or to see you home after activities until you feel relatively assured that your ex has calmed down. And definitely don't go anywhere with him, even if he's being apologetic and acting like the model citizen.
You might want to call the 24-hour National Domestic Violence Hotline at 1-800-799-7233 (SAFE) for counseling and more information, or see gURL's section on dating abuse for help.
I wish you all the best.