Three year old waking shrieking, gagging, and clawing at her mouth. Any advice?

No it's called Night Terrors" It's a common sleep disorder in toddlers. It usually stops when they are about 4-5 years. Here is a link Below. Hope that helps. And what you described DOES fit night terrors, they see insects and snakes sometimes in dream hallucinations, even with their eyes wide opened.