my husband cheated

the past weeks I noticed my husband very "weird" using his phone. Facing the screen just to him and sitting against the wall always. I asked him 100 times was going on. 100 times he answered nothing. Last night while him and my 5 month old baby were sleeping I checked his phone. No texts, nothing weird. Until I opened his Instagram. He had one with a fake name and just 2 followers. I saw the messages. He is being talking to a 25 year old girl for a while. Sex conversations, about fantasies, exchanging intimate pictures, etc, but that wasn't the part that destroyed me. He was telling her about me, about how shitty I was. We haven't have sex since the baby was born. I had a really hard natural birth and lots of stitches. I was in discomfort for many weeks and he knew it. I also didn't have any desire to have sex. He was telling this girl that I was a bitch and 1000 other bad stuff about me. I didnt fight, I just asked him to leave the house. He said Im distroying this family, and that my baby not having a father will be my fault. I dont trust him at all. Last week he went on a business trip for 3 days. God knows if that's true. I dont want him to be alone with my baby either. I know Im doing the right thing, because there is no way I can share the same roof with him. I love my baby more than anything and I dont want her to suffer or to watch endless fights. I'm holding in there, but idk what else to do. UPDATE A ND QUESTIONS. Thank you for the support. Im at stay at home mom right now. All my family lives 5000 miles away, so idk what to do to go back to work. My husband promised me he will still give me money for me and my baby and keep paying the mortgage. I dont trust him and Im afraid this situation will stop at any minute. Can they take my baby away for not having an income? I am an US resident (Im waiting for my citizenship).