That might very well be the case, but only right now. You can earn back trust if you have done things to lose it. Not an uncommon condition for people like us at the end of our drinking days.
Please don't drink. It will only confirm for him once and for all that you are not trustworthy and you will be back down the rabbit hole.
He will trust you again, in time, by you showing him - not with words but with actions - that you can be trusted.
You also deserve to be respected. If the trust is gone, then it is gone, but you don't need to be kicked too often while you are down. You get to live a peaceful life, just like he wants to. It is a delicate dance. At some point, you might need to tell him that unless he has concrete criticisms, he has not other choice but to trust you that you are taking your meds. Random checks are traumatizing and I think cannot be a part of a healthy relationship.
Stay sober. You are doing so well on that front.