You can certainly say
She flung herself at the transparent door.
but this would imply with some force, and possibly intending to cause damage. For example, suppose someone is trying to get through a locked door:
He threw his entire weight at the locked door, but it refused to budge.
Here it's clear he is trying (unsuccessfully) to force open the door with his body.
Meanwhile, "against" implies impact but not necessarily with significant force. Throwing yourself against something instead implies strong emotion of some kind, but no intent to break that thing.
An example (from "Gone with the Wind")
She threw herself against the opening door as he was walking out. "Rhett, if you go, where shall I go, what shall I do?" she cried.
"Frankly, my dear, I don't give a damn," he said, then strode away without looking back.
In this scene, Scarlett isn't trying to break the door, but she is very upset.