You are in a dangerous situation with an emotional abuser who has used your son as leverage to manipulate you and the police have done nothing. You need to leave. You need to seek help from a domestic violence shelter ASAP. I am so sorry this is happening, but it is not your fault. I don't know why she is acting this way or if it will change, but emotional abuse rarely does.
She has made serious threats to harm herself and your son. She should have been Baker's acted - taken under psychological observation in a hospital for a few days to determine if she needs longer treatment, as she has made a threat to harm herself. I don't know why the police didn't intervene, but this is scary. I am afraid for you.
She may be experiencing post-partum depression, since you have seemingly indicated her emotional state has recently changed. It is very serious, regardless of whether you think she's normally capable of doing the things she has threatened, or not. Your responsibility is to protect your baby at all cost, and above all else. If something - anything happens - if she attacks you physically or anything at all, even if the child is unharmed in the event - and the police come, DCF will investigate and you will be found to have stayed in a situation where your child was unprotected. That means the child may be taken from your care as well as hers. It would be very hard to get your son back if this happens.
It would be ideal to talk to her about seeking help on her own, without intervention, but I don't think it's wise to take a chance of arousing her emotionally in the state of duress she seems to be experiencing - **especially** with your child present. Is there anyone you can call or appeal to who might help? You need family and friends around - even a neighbor may be a good advocate. She needs to have help, but your immediate responsibility is to protect yourself and your baby.
You are NOT at fault. She's probably not even cheating - it sounded like a ploy to make you jealous or insecure as some emotional blackmail, but even if she has - don't give any attention to it. You cannot play into a game that will only escalate. You are not terminating your relationship right now, you are not kidnapping your child from her or anything else, so you don't have to feel you're doing anything except what you have to - right now, for your safety - you need help. It's the right and only thing to do.
I wish it were easy for men who need help to get it, but there are less resources even for men than women - they cannot be housed in the same protective facility as abused women. Sometimes the shelter does have hotel vouchers at least to remove you from the situation for time for it to de-escalate emotionally or for you to have time to find a place to go or remove the abusive from the home so you can return. Please, if you can, just leave - if you have money for a hotel room, or relatives to stay with that would be ideal. Can you search for resources and call them? Do you need help locating numbers or anything? Don't confront her - don't give her any warning while you're still there, alone. Please call someone for help. If you need help locating resources and support, I will gladly help all I can.