My boyfriend is deleting messages AND search history. He also lied straight to my face for months about looking up his ex girlfriend. Are we doomed?

Anonymous
The other day I nonchalantly asked my boyfriend, if I looked at his Facebook search history would I be upset with it & he said no. He pulled out his phone & showed me a few & then hurried past a girl. I called him out on it. First he tried to lie & say that she popped up but obviously she's on the SEARCH log because you searched for her so he said he wasn't even friends with the girl. He didn't even know her. So I let it go but it had been bothering me. I brought it up the next day & just asked him who she was. He said we should have looked at when exactly it was that he looked her up in the first place. I said ok well lets go to the history of your search log & he tried to act dumb about it like he didn't know there was one. But he sure found it real quick for someone who didn't even know what it was. Right when he opened it he was like I accidentally hit something, she's gone now. Total bs. So I'd been having a weird gut feeling lately about him. Not really sure why and had really no reason to be. So after this I grew suspicious. A couple months back I caught him looking up his ex girlfriend. He said it was a one time thing, he was just making sure she had a deleted some pictures of him she still had. I accepted it because I trusted him & moved on. I pulled a no no & looked at only his browser history while he was out of the room. Turns out he had a very long history of looking her up almost everyday to date. I brought it up to him, admitting I invaded his privacy but I was so upset about it, I couldn't let it go. All this time he's been lying to my face & making me feel crazy for having a weird gut feeling & he's been doing this. He said it was only because of the way she left him. He wanted her to suffer the way he did & the only way he'd know that was by looking her up. I let it go (kinda, obviously) because I love him so much but I'm hurting now and I'm self conscious. Obviously he can't be trusted for his word. How do I go about this? Help. Should I end this?
My boyfriend is deleting messages AND search history. He also lied straight to my face for months about looking up his ex girlfriend. Are we doomed?
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