I don't think you should end the relationship, it sounds like he tries his best to reassure you that he wants to be with you. How bad and how often are you fighting? I think most of your insecurities are normal, but it sounds like the high anxiety is what is making your relationship difficult. You need to take a step back from these emotions and remind yourself why you two are together. Pay attention to the positive aspects of your relationship and take him at his word when he reassures you, and when he says he loves you. Having sex daily is great! That's another positive! It sounds like you feel as though you don't deserve a happy, healthy relationship, and somehow you are subconsciously creating ways for this one to fail. You DO deserve to be happy, and to be with someone who treats you right and who loves you.
It also sounds like you are bringing past relationships (yours and his) into this current one. You're bringing the same anxiety you had in previous relationships into this one, and it's causing you trouble. I think you need to learn to let go of the past, and the pain, and give gratitude for the good things you have in life. I understand having anxiety, especially in a new relationship because being vulnerable and falling in love with a new person is the scariest thing you can do. Trust me, I get it. But you can stay in this relationship and work through your anxieties at the same time. Generally, I am quick to give the advice of being single and focusing on yourself before getting involved with someone new, but this is a little more specific. Your feelings and emotions are normal. Feeling jealous or feeling anxiety is completely normal and valid, and human... it's what we do with those emotions and how we react to them that can manifest in unhealthy ways. I think if you are able to learn to let go of some of these stressful emotions, that it will greatly improve your current relationship.
"Caring is not an advantage."