Letting baby cry herself to sleep for hour going to make her emotionally damaged?

We have a newborn daughter. She had to be emergency delivered early by 5 weeks because my wife's cancer came back. (Stage 4 melenoma - lungs, liver, and spine). As a father I'm trying to parent my other two kids (4 and 6), take care of the newborn, and take care of my wife.

Grandma comes over to help during the day Monday- Friday. The newborn is held, fed, bathed, and loved. But at night, no matter what I try she just screams for an hour. She's clean, been burped and fed. Not too hot, not too cold. I've bounced her, rocked her, sang, swaddled, patted, rubbed, everything I can think of. Is just letting her cry after I've done everything going to cause her to be emotionally stunted? My wife thinks so, but I can only do so much. I feel so guilty when she cries because I'm emotionally empty, angry because nothing i do works, sad because i never seem to be able to help.

Any other parents have life experience with this? Did you do it with your kids? How did they turn out? Like I said 90% of the other times, she cries and someone is there right away holding her, and loving her. It's just that hour (longest has been 1.5 hours) at night.

Edit:

Thank you all who were helpful. I'm getting a baby wrap and a yoga ball. Yes, we use pacifiers and white noise. To those who criticized or condemned, I kindly say, "Dude or dudette, be nice." We are all trying our best as parents.