Boyfriend doesn't trust me b/c my past sexual relationships

I've been dating my SO for only a short period of time (few months), but very recently we've become "official" (FB official..., bf/gf, etc.) He has made it clear that he does not trust me, and although he admits it is his own problem and I can't do anything to fix it, I am constantly worried that he will leave me if we can't establish trust right now.

We were introduced by a mutual friend, one who I had casual sex with (under the influence). I had a drug/alcohol problem for a while, and this went hand in hand with my casual hookups and one night stands. However, my boyfriend does not view sex as something you can have casually, and he would never continue a friendship with someone who he had slept with. I always found it easier to pretend like my casual sexual encounters never happened, and even continued friendships with some of the people.

When my boyfriend found out that the mutual friend who introduced us had slept with me, he was incredibly upset, to the point where he almost threw up. I had hooked up with that friend very closely to when I met my SO, and this made him feel like I was being "pawned off" to him by our mutual friend. I wish I had never met him in such an uncomfortable way, but I can't change the past. I do not talk to anyone who I have previously hooked up with anymore, especially after meeting my SO for the first time because I was so incredibly intrigued by him. I become infatuated with him off the bat, but this turned into love after we started dating.

He assures me that we are fine, and he is still coming to visit me for a late valentines day celebration, but I can't help feeling anxious. I've never felt so comfortable with someone, on an emotional, spiritual, and physical level.

Right now I am sober, and I don't have contact with any exes or past hook-ups. I feel completely stable and I know I am true to him.

Does anyone have advice for things that I can do to build the trust between us? No matter how many times I tell him I am faithful, he still is worried I am flirting/talking to other guys.
I really don't want to lose him.

Hang in there girl! And congratulations to you for cleaning up and finding a true relationship!! That is no small thing! Heres the thing... it sounds like there really is nothing you can do to fix this, unfortunately. have you had a face to face talk with him to give him reassurance and to look him in the eyes when you reassure him?
Aside from that, your past is yours, its not something you need to apologize to him repeatedly about. You didn't do anything wrong to him. I suggest you just keep reassuring him he has nothing to worry about and hope that he can accept it as true. Kinda sucks that he says he doesn't trust you... really that's a shitty thing for him to do, like he is punishing you. We ALL have our past mistakes, our past traumas, or past wild oats sewn... whatever... I bet he will get past it and you will be just fine together.
If he doesn't.... reach out for help please. Be strong and stay proud of yourself for how far you've come. Relationships are never easy until the RIGHT one comes along, so if he cant handle your past, just know that the RIGHT one WILL be able to handle everything!