To look down her throat, it's not that hard, truly and it's something you really need to be able to do so no time like the present to learn. Pick her up, wrap her in a little towel, like a dish towel or whatever you have. Sit on a chair in a bright place with good light. Sit as far back as possible in the chair, and gently put her facing you, between your legs to try to hold her (assuming you're alone and have no one to hold her for you). Take one hand and using your index finger and thumb, grip her upper beak. Do the same with your other hand, gripping her lower beak. Gently (and not open too wide) open her mouth a bit and look in. I'm betting you'll see either nothing or bubbly spit.
You need to do this to eliminate as best you can the possibility that she's got something stuck in her throat. This will just make you stop worrying that she's gagging on something. If something IS stuck in there... you can try to get some cooking oil down her throat to get whatever is there to slide down. Or, if it's something she should not swallow, I'd maybe try using tweezers to get it out if it were me. I've never done this but this is what I'd see if I could get to work.
If you can't see anything in her throat, I'd go the antibiotic route as it's probably a respiratory infection. This was the advice I got from the University of Kentucky poultry experts when my chickens started having symptoms similar to yours. I bought my antibiotics at
Tractor Supply for about $5 U.S. dollars. I used
Duramycin-10 antibiotics (tetracycline) but other antibiotics work too.
I don't know what to tell you about the white runny poo. So many poos that look horrible are normal so I can't tell without a picture. I use this web site a lot to see if what I'm seeing is normal or not. It might help you.
http://chat.allotment.org/index.php?topic=17568.0
Hope this helps,
Guppy