First-time stay at home mom

I just had a baby 2 months ago. Being a first-time stay home mom put too much stress on me. I really miss working at my job I use to work at. My former boss wants me back miss me. I told my boyfriend about it he tells me its not the right time for me to go back to work since our daughter is too young and she only almost 3 months old. He works a full-time job as a manager. I'm not used to be a stay home mom. I'm depressed and feel like being home is boring all I do take care of our daughter all day, and cleaning, and doing laundry while he working.

He only takes care of her 3 hours before work when he wakes up at 11 am until he goes in at 3 pm. 3 pm I take over all the way until midnight when he gets home. He takes her for 1 hour goes to bed. I usually sleep decent but he gets so mad at me waking him up if I got an issue with the baby, or I need run errands 7 or 8 am morning if run out the formula milk, or I need him to take over at 10 in the morning while getting some rest and wants me to wait till 1130am. He gets cranky all the time.

I want to work so badly feel like missing my co-workers but my boyfriend tells me if want to work I have to go do split days that I can't work nights and I cant work Monday and Tuesday. I have to work Wednesday, Friday, and Sunday those splits days. I told him not sure if my boss would do that. He says you can work 8-2 but he complains about me working 20 hours will be too much. Split's days he tells me he doesn't want to wake up with baby back to back early in the morning if my schedule would be straight 3 days if not splits days.

I kinda feel like I'm stuck not sure what to do. What is your experience staying home mom? Do you think back to work will be too early for me to go back or should I wait till she maybe a year old or so??