My fiancé lied and I’m hurt, please help?

So I’m a stickler when it comes to lies, my fiancé has always been honest with me except about 1 thing; porn. Which that’s cool that he watches it, I just don’t want any lies. I had a relationship prior to this that was full of lies, and I’m constantly paranoid anyways. So he knows how much honesty means to me. Well, he first lied to me a year ago about porn. He then seen how it hurt me and promised to never lie about it again. Ever since, he has told me each time he has watched porn just to build that trust with me. 

Today, we were looking through movies on his phone and we saw porn in his history. He says ‘omg I must have done this in my sleep, I don’t remember’ but it was like 20 links clicked, and I was like ‘no dude. You’re lying.’ He continued by swearing on my life, my dogs life and his own. I’m very superstitious so I take those things very seriously. Then, later that night, after I never fell for any of the lies, he finally tells me the truth and says he ‘clicked on it when he was half asleep and barely remembers but does remember when he closed out of them.’ So here I am, wondering if that is even the truth, and wondering if I should be with him since he’s broke trust with me again?

He offered to put some type of porn blocker on his phone and give me the password, but I don’t wanna be a babysitter. I love him so very much, but I’ve just been hurt so much. I’m not sure what to do. I feel like I’m constantly going to be paranoid. Any thoughts?