Is this normal or do I have a Postpartum Mental Illness?

I don’t know if I am depressed or if this is normal. My son is 1 month old and has colic. From 11:30pm to 3:30am, every single night he is crying not stop. Nothing soothes him. Walking him around, rocking him, sound machine on, and even driving with him doesn’t work. He just screams and cries. I feel during this span like I am a bad mom. I just want to hand him to my husband and leave the house to never return. During this span of time I am exhausted and super frustrated I can’t help soothe him. During the day and after that span where he falls asleep I am a okay and happy. But every night I get so unhappy and just feel miserable. Any advice?