I started studying martial arts when I was 7 and it's something I've been consistent about most of my life. I'd recommend that. It would not only give you skills to defend yourself, but also help with your self confidence. If she can go too, that's even better.
Legally, I don't know what kind of weapons are available for home defense in Algeria. I know in places that don't allow firearms, bats or sticks (baseball, cricket, hockey, etc.) are fairly popular and not seen as out of place when left around the house. I have a friend who keeps a machete around. Where I live, we can have guns, so I own several. I would say whatever you decide to get, make sure you're comfortable using it. There's no point in purchasing something that you couldn't effectively use.
I'd also say, if you both care about each other, this should be something you can let her know you're concerned about. She may have some ideas on what you could do or try.