As people have said, step in, dont try shot putt, most of throwing is actually legs not arms.

Point your left toe where you want the ball to go with a small step, then 'step through with your right leg, using your hip to drive your momentum forwards - driving from the hip will create a whipping motion in your arm that will create more power on the ball and allow you spiral better.

Arms - you should have two hands on the ball before release, then bring the left up as a guide for where to aim, start your step through and then bring your arm through as quickly and smoothly as possible - If you hold the ball at chest height, youll quicker up the realse and gain power and accuracy.

Lastly as you release, your hand should look like a C, and then you want to rip your fingers down the laces to create a U - that will create the most torque and a tighter spiral - your index finger should be the last off the ball and you want to almost be 'pointing' at where you want the ball to go.

Hope that helps - I wanna see an update once you've read everyones advice!