<human>: Can you condense the text into a few key points?

First a little back story...We moved in with each other after about a year and a half of dating, which has worked out pretty well. One day after taking a shower about a year ago, I walked in on him looking at... Well you know. Except...they were preteen models. I expressed how it severely bothered me, and he stopped after many lies and long talks. I discovered that he also liked to look at girls on facebook... Which I didn't mind, but some were my closest friends and people we worked with. I can't look them in the eyes to this day. 

He has lied to me more times than I can count about the 'models' and facebook girls, so it's hard for me to trust him when he says he's done with that. 

I have major trust issues with him because of the past, so I tend to check his phone regularly to make sure he isn't looking at the 'models.' I know it's wrong but I can't stop... If anyone had or has this problem advice would be appreciated.

On to our current problems. We hardly ever have sex. Being 20, this is a big deal for me. I'm young and want to enjoy it. I've always known he has a lower sex drive than most men, but what bothers me is that he never seems to initiate anything, I always have to be the one to do it. I work really long hours. He says he 'gets bored' and just helps himself when I'm gone, which is fine, but it takes him a day or two to completely recharge, and so I get left out a lot.  

I came from a family that was very broken and I suffered from a lot of depression. I'm still incredibly self conscious, and I just don't feel like I'm wanted, I feel like I'm just there to help him when it's convenient. All I want is to feel wanted occasionally, but he doesn't try. I've talked to him about this multiple times and have no idea what to do. I don't want to leave him, but this has been a problem for a while and I really want to try and fix it.
<bot>: Boyfriend has low sex drive and helps himself out more than me, and I have trust issues and can't stop checking his phone.