Boyfriend thinks I slept with his cousin...

I posted this but accidentally deleted it so here it goes.

About 3 years ago me and my boyfriend hooked my sister up with his cousin. (They broke up a few months later). At the time they were together me and my sister lived together and worked together. Well she ended up dropping her phone and shattered the screen so bad every time she would use it she would cut her hand. I started letting her use my phone when she needed. I had no problem we help each other out all the time.

One day we were at home and we kept passing my phone around because I would log out of my Facebook and she would log into hers so she could talk to her boyfriend. I finally told her to just send him a friend request on my page that way neither of us would have to keep logging in and logging back out. Every time he would message he would always say “Hey is your sister around?” I would throw her the phone and that’s that. Well they eventually broke up and I never thought anything else about the messages and she started a new relationship with the guy she’s with now. Also keep in mind, when I was letting her use my phone it was only for a few days until she bought another one.

Fast forward to 6 or so months later I let my boyfriend use my phone, he found the messages on my messenger and immediately thought it was me and accused me of sleeping with his cousin. I told him I let my sister use my phone and he never believed me. That night I called her crying because we broke up over it and she offered to call him to clear things up but he never would answer my phone. We got back together a few months later and it was never brought up again. Him and his cousin are still super close.

Fast forward 3 years later to last night he was laying on the bed and out of the blue he brought it up again started calling me a hoe and accusing me yet again of sleeping with his cousin. (I never wanted to call my sister about it because like I said she was in a new relationship and I never wanted to start things between them over something stupid) well last night I got tired and I called her, put her on speaker and she told him everything about her using my phone at the time and me being nice letting her use my Facebook because she didn’t have a phone. He still did not believe me after she told him, she even told him that I’m her sister and I would never do anything like that and he’s stupid for not believing her or me. So after the name calling I packed up all my things, grabbed my kids and we stayed in a hotel last night. We are going to my moms house today because I can’t keep being accused over something I proved to him wasn’t true.

I guess my question to y’all is, was I wrong for not telling him I let my sister use my phone at the time? Was I wrong for leaving?