My boyfriend lied about watching porn and I feel like killing myself, please help?

Firstly, see your doctor about your depression. You have been depressed for a long time, and it's impossible to sort things out in your life while everything seems so bleak. If you dont already, then socialise a bit with other young mums in your situation by going to Mother and Toddler groups nearby. If one doesn't suit you, try another, I didn't like the first one I tried when the health visitor suggested it, but I found another that did suit me, and I enjoyed the company (plus it really tired my son out, so I got to rest afterwards). See if you can make friends with another mum, and swap babysitting with her, so each of you gets a morning, afternoon or evening totally to themselves every week. Even a small amount of time to think only about yourself rather than the baby can be very refreshing and help clear your mind. If you feel desperate to save your relationship, then go to couples counselling. If he wont go then go by yourself, it will still help. With things getting as bad as physical violence I'd just leave, if it was me, but it's up to you. Improve your life in whatever ways you can, and try to get into couples counselling, and see if maybe with the help of a professional you can sort out some way of being together that's better than this.