Having a mental illness does not give someone the right to be controlling and abusive to their partner every day. Being a loving partner when ill means doing all you can to be part of a team working to manage the illness. Instead, your guy is trying to manage you.
You didn’t tell us whether your boyfriend is in treatment. If he isn’t, you are not obligated to put up with his demands and his paranoia. You cannot and should not be more interested in managing his illness than he is. Without treatment, this is not likely to get better – no matter what you do. You will always have to be on guard lest you trigger his jealousy.
If he is in treatment, I think the best approach is to join him in sessions with his therapist so the two of you can work out how you can be be supportive of his healing without compromising yourself. The two of you may also find attending programs run by your local chapter of NAMI (National Alliance on Mental Illness) would provide further support. They run programs for people with mental illness and their families.
You’ve only been together for 5 months. From what you shared in your letter, it looks to me like this relationship is too unequal to survive. Do consider taking a big step back, especially if he isn’t actively involved in his treatment. Learn more about what it means to be a supportive partner for someone with mental illness. Before you get more involved, see if he is willing and able to be a team.
I wish you well.