Please help! Just had a baby, relationship advice

Hello,

I’m 27 years old and I just had a baby with my BF of 3 years 7 weeks ago. My BF and I live separately. He is 30 years old and lives 5 minutes away. He lives with his grandmother who is 80 years old and states that he doesn’t want to move out because his grandmother needs him. Other family members live with his grandmother as well but they don’t really look after her. However, she has a home health aid to care for her during the day. My BF also spends the night at my house almost everyday. The problem is he thinks it’s ok for him to come to my house as late as12am after I’ve had to deal with a screaming baby all day. Then he leaves for work at 8 am. He helps with the baby overnight but sometimes he’s so tired he doesn’t even hear the baby cry so I have to tend to him. My BF still goes to the gym or hangs out with friends and comes to my house at anytime he wants. Sometimes he will tell me he’s going home for the night because he needs a break and I’m the one that’s always with the baby. Tonight he went to the gym directly after work and didn’t even tell me he wasn’t coming to my house. I haven’t even talked to him since he got to the gym and I dont even know where he is. I’m just so frustrated because he told me that he was ready for a baby but he still has to be at the gym or hanging with friends for hours several days during the week. My baby is only 7 weeks so I thought it would be different. When my son was 4 weeks old I went to my mothers house for 2 weeks so she could help me with the baby. My BF came to pick up my son & I. While my son and I were away my BF was talking to another woman and exchanging nudes in his phone. The woman knew about me and that we just had a baby. He claimed that he didn’t have sex with her. I forgave him because I wanted to keep my family together because I just had my son. I just feed so stupid. & I’m also regretting having a baby because it’s hard to do almost everything alone. I don’t have any family where I am and no one really to talk to. I could go on and on but I’ll stop here.