My first real panic

It would appear one of my 2 fat ladies is egg bound.  She is the one that doesn't lay eggs unless you count the 2 shell-less ones she laid not long after we got her (about a year ago). 
Last week she actually laid a 'proper' egg but it was the size of a bantam egg, so tiny and bullet shaped. 
Last night I saw she was just standing about under the tree looking pitiful, all puffed up and not doing much and she wasn't for joining her lady friend in the coop so I picked her up and put her in.
This morning she was still the same, but she came out of the coop and made a very yellowy/mucousy (probably not a word but hope you get the picture - and not too graphic a one at that) poo then went to stand under the tree again.

I brought her in and gave her a warm bath, dried her off and put her in a carrier with some hemp a bit of food and water.  She is still there looking sorry for herself and I can't help but feel sorry for her too.  I am hoping I have done the right thing and I plan to leave her there overnight (I think this is the right thing to do but I am open to any advice as usual).

If she is still like this in the morning I will take her to the vet but fingers crossed she will be right as rain soon.

ANHBUC you were correct.  I checked her this morning and there was a lot of 'gooey' stuff plus yoke in the bottom of the cage.
She is a lot better today so I put her back in the enclosure and she headed straight for the water and drank for ages. I gave her porridge made up of layers pellets and a couple of (mini) shredded wheat.  She had a few mouthfuls and also made a half hearted attempt at foraging but I think she is over the worst now.

I will keep an eye on her today but I think it is fair to say she looks much better and happier than she did yesterday.