How can you cope with a girlfriend that thinks you’re cheating on them all the time?

My gf thinks I’m cheating all the time. We live in our own places. We don’t own these places. I live with My mother and grandma in a house. She lives At her dads. We got kicked from our apt. My name is messed up and so is hers for apt. 

True Things that happen

1. My grandma turned a room and restroom into a mini apt. It’s completely sealed off. A girl tenant moves in and my gf thinks I’m already cheating on her with tenant. Not even 1 day after she moved in too. About 1 year passed and she still thinks I’m cheating with her. Never even went to her place or even talk to her. 

2. A fake girl adds me on SC, and says “hi handsome” etc.. turned out it was one of those girls that do live cams and my gf thought I knew her just cuz the girl actually did reply back to her text when my gf questioned her on my Snapchat. This was in Vegas. Messed up hours of our trip. When this girl added me I told my gf immediately.

3. About 5 nights ago a girl adds me on Facebook, you know those girls that look like models which are fake accounts? I didn’t bother to confirm. Next thing you know my girl texts me and says “why did you follow her?” Like how can I follow someone who isn’t my friend? There was no follow option on that person either. 
4. Thought I messed with her best friend. 
5. Thought I messed with one of the apt manager ladies
6. Thought I messed with a big fat fat girl who worked with me.

My girl look like a model. Don’t need any other. She’s too pretty to be insecure.