Run... NOW... and don't look back!
I don't mean to sound so negative but it's NOT going to get better. You've only been together for 5 months and it's already this bad?! Imagine what it will be like in 5 years. You're going to be on lock-down, hon. He doesn't even want you to spend time with your family. Not a healthy relationship at all.
Technically, it's emotional abuse. There's a pattern... blow up at you for no good reason, then apologize and build you up... repeat; isolate you from friends and family; make you feel unattractive, as though no one else would want you, etc.
There are sooooooooooooooooooo many options for you out there. Don't fool yourself into thinking that you won't find someone else. You WILL and it will be better.
And to answer your question: NO, it's NOT worth it!! Don't waste another minute.
Good luck!!