Feeling so self conscious

Iv been with my BF for 10 years. We have 4 children together. We have always got on so well, barely argue and have had a good sex life. However since having twins 4 months ago and also through most of my pregnancy we have not had sex at all. I am exhausted, I’m exclusively breastfeeding the twins and running around after our other two kids all day. I have also been diagnosed with BV after having the twins but I can’t take any meds for it until I stop feeding so down there isn’t a place i want people going near. I also just don’t feel confident in my body after the twins. I put weight on, I am however losing the weight and really I don’t care that much as I think my kids are totally worth a few extra pounds and extra lumps and bumps. Every day I make an effort to look nice, i wash, do my make up, try and dress my best as keeping a good appearance is important to me. My partner is at work from 6.30am to 7pm. I have the house clean and tidy and his dinner on the table for him every night. My partner never praises me with the kids or mentions my weight loss, instead he just points out to me that I shouldn’t be eating that ice lolly after dinner or having a biscuit with my cuppa, and hints that I should do more exercise. Anyway I know my partner has been feeling sexually frustrated but Iv explained my reasons for not wanting to have sex. He does still pester me often to have sex or just do ‘other’ stuff. So the last few days he has been working away, he arrived back yesterday. It was midnight and i was feeding the twins, when doing so I normally scroll through my phone however it was dead and taking a while to turn on, I reached for my bf’s phone instead to then come across a website made for people wanting to have an affair. I instantly felt sick that this thought had even crossed his mind to actually look into finding a website online to cheat. Who knows if he’s signed up to it or not. I then became a paranoid wreck and found myself searching for whatever else I could come across. Which was lots of watching porn, consisting of big boobs... iv got really little ones and Anal.... NO WAY! It hurts too much. But clearly what he likes. I now feel even more self conscious as I find my self comparing my self to these pornstars and just think he will compare me to them too. I feel very hurt and like I never want to have sex with him again or even see me naked. Is this why he’s been on having an affair website?. How do I approach him about this or are we just doomed? I feel like he’s already destroyed my trust for him. I just want to mention he has always been a great dad and he also just so so sensible it actually makes him a bit boring. But I like this about him after ha experiences in previous relationships. I think this is why I’m struggling with this so much as it’s a massive massive shock that he would do this. I would just like to know others thoughts on the situation?