I feel like a bad mom

I feel like I can’t do this. My son is only 3 months old and he’s in this phase where he just cries and cries and nothing I do makes him happy and if it’s not that then he’s bored every 5-10 minutes and I have to keep him entertained. I literally don’t get time for myself nor time to ever get anything done and it just seems to be getting worse with everyday. I’m getting too overwhelmed and I end up crying about 3 times a day because I feel like I can’t do this. A lot of the time he just wants to be walked around except he makes my back hurt. He’s really heavy and big for being only 3 months. It feels like I’m losing my mind and I’m starting to lose my patience. I try to make him happy but they’re times I just let him cry for like an hour in a safe place because sometimes I just can’t do it. I feel like I don’t even have time to breathe. I don’t feel normal. I don’t feel like myself. I love him with all my heart but I can’t help feeling that maybe I’m just not cut out to be a mom. I would never give him up or harm him but I just feel like I can’t be a good mom. I know it won’t be like this forever but at the moment it feels like it will be. I’ve been dealing with this 24/7 for a month it feels like now. I was told it’s probably a leap, but can they last that long? I try so hard to be there for him and comfort him . .