Every player starts out throwing nose up into the sky for some reason.
The drill I have people do is pick a spot 40' in front of them on the ground and hit it with a full throw. Really, throw your disc at the earth. Once you can do that consistently, aim for a spot 60' out. Hit that with consistency. Then move to 80', and so on until you are throwing level shots by default.
It has much more to do with your arm throwing plane than it does a thumb or anything in your grip.