Your boyfriend’s jealousy is his to manage and deal with. You’re not going to convince him. My experience in this area and research on it shows that even if you alter yourself in some way to appease him — he’ll just continue to condemn you. This is because the distortion is his to fix not yours. I would do three things.
First, I would start talking about your own feelings when he accuses you. Rather then explain and defend yourself begin talking about how hurtful it is not to feel trusted. Let him know he’s not the only one in the relationship that gets to have feelings.
Secondly, be very clear that his behavior directly causes your reaction. In other words, point out that the thing that makes the relationship difficult is his mistrust, blame, and criticism of you.
If you do go to couples counseling I would be very clear with the therapist that your boyfriend’s jealousy is destroying the relationship.
I would not wait to begin dealing with this. Men with these kind of control issues and jealousy tend not to improve on their own. They keep finding reasons and rationale to blame, condemn and mistrust, and they try to micromanage and over-control their girlfriends and wives.
Make an appointment with a couples counselor but make it clear and he needs to be doing his own work on this. If it doesn’t improve in a few months, you may want to consider moving on.