Hi there,
I have a 15 month old too. And same thing for about 1 - 2 weeks, she would wake up screaming at the top of her lungs. When we picked her up, she would stop crying but would bawled loudly/scream as soon as we tried putting her down along with clinging to our arms tightly. I thought it was separation anxiety. But in the end, it turned out her molars were coming in.
Hang in there. It only lasted us 2 weeks and then the molars proved that it was the cause.