Yes, do look down her throat. You will see a number of things.
This most obvious will be a small opening at the base of the back of the throat. This is the wind pipe. Check to see if there is a red tinge to the opening. Check for gape worms and finally check to see that the opening is closing slightly with her breathing.
If this is good, then you will have a chance at finding out what is wrong with her. Chickens put thier heads back, use thier tongue, to close the wind pipe when they drink . She may have mucus in the mouth or nasal passages. Check this out. The roof of the mouthg will be "split" with a part from the back of the beak to the front. If you do not see this, then you need to pull whatever it is out of this. I have have numerous chickens with this space blocked by a forieng object or crusted nasal discharge.
