should I ask my boyfriend about this girl who likes his status

So I don't know if I'm just being paranoid but there is this girl who always likes my boyfriend pictures and status on Facebook (me and him aren't friends on fb I just "spy" on him from time too time. ) everytime I see her liking something of his I get a gut feeling. The other day I saw where he had posted about him being single, so I texted him telling him I was going to break up with him. But he assured me it was his cousin to keep me from breaking up with him. Which is weird because I always ask for his password but he never gives it to me. Yesterday he said " cell phones break up relationship, you might see a girl that got my number somehow and think I'm texting her". An I said " cell phones only break up relationships if someone is hiding something"...he didn't say anything after that. I constantly ask him if he is being faithful and he say "I'm just chilling"...he claims that means he is being faithful...I'm extremely scared of getting cheat on/played that's how all my relationships turn out. But I'm madly in love with this boy I drove 3 hours in a thunderstorm to see him. I do everything I can for him to make sure he is happy. I don't wanna be heartbroken. What should I do?