Absolutely. Your horse, through throwing her head and chomping, is communicating to you that she is in discomfort. The nutcracker action of the snaffle which you have focuses pressure on the roof of the mouth (hence her throwing her head up to avoid the pain) and pressures the lower gums and can pinch the sides of her tongue depending on the shape of her mouth.
For starters, I would consider either a plastic/rubber mullen bit, which evenly distributes pressure on her lower jaw, especially the tongue.
Or if you prefer, a lozenge bit reduces the effect of the nutcracker effect on the horses upper jaw.
Try to keep the bit you use as light as possible. Personally I broke in my youngster bitless with a hackamore, since she despised the bit so I listened to her and tossed it to the side.
Do what is best for your horse and your horse will appreciate you for it :)
Go for a lighter bit or one with a different action, or if you're prepared to then go bitless.