The fastest growning group of gun owners is women. There is no reason for mentally healthy women to live in fear.
See the local NRA group, certified teachers will teach you about gun safety, laws involving self defense with guns, and help you learn to shoot well, which is a prerequisite for a carry permit in those states which allow it.
Then, get the permit and carry legally.
A few years ago, a female health practitioner testified before Congress in hearings on gun control, that she lived alone in a two story house.
One night, she was woken by noises of people in her downstairs rooms, clearly they had entered illegally, and were rummaging through her stuff.
She took her M-16 (it might be called AR-15 in civilian version, I am not sure,but most folks still call it an M-16), and racked it.
That means she pulled back the bolt, then released it, which automatically picks up a bullet and installs it into the chamber, ready to fire.
Racking a semi-automatic weapon makes a distinct sound, which cannot be mistaken for any other sound that I have ever heard.
The burglars also recognized that sound in the dark. They screamed with fear and jumped out windows and ran off.
Without a shot being fired.
If she had been unarmed, what are the chances they would have raped her? I'd say pretty high.
For urban dwellers, I actually recommend a pump 12 gauge shotgun, military style, they are lethal if one has to shoot within 25 yards, and much safer for neighbors. A pump shotgun also has a distinct sound easily recognized by most burglars, even if it is different sound than an M-16
But, with the original ammo, VN war style, M-16 bullets also usually becomes harmless as soon as it passed through anything, even dry wall, because the soft bullet fragments very easily, even on drywall, etc.
Newer M-16 ammo will penetrate better, thus is less safe in cities, and also has less kill power since it passed through a body in one piece.