Definitely tough to listen to that kind of crying/screaming! Don't feel like a failure, lots of us have had kids like that!!
Last year I had a little girl (15ish months) start and we bonded very quick and were very close. She would cuddle with me all day. She started not wanting to go home with mom/dad/grandma and when she would turn from them and say no and grab for me, I saw the hurt on their faces and knew I needed to curb this behaviour!! She would also scream bloody murder if I cuddled any other child.
I had to decrease our cuddling time and be firm about it. It broke my heart but I had to just let her cry and encourage her to play with her dc friends. It eventually got better!! She still sometimes gets jealous if others cuddle me but I just tell her that we'll cuddle when xx and I are done.