:DAh .....you think the goat may have lice, so are using the shampoo to get rid of them ....not cos you want a brilliant white goat!!
In that case, the shampoo will not get rid of the lice, but of course make the goats coat smell good. What you need is Farmyard Louse powder, which can be used on all livestock. I have the organic stuff. You can get it from the animal feed shop usually. Its the time for lice, Cain and Abel have just been done with the powder, as they had rubbed bald patches on the top of their backs. I always give a second application of the powder, to make sure the lice are gone. But it works.
If you goat likes a bath then carry on, but I would do it when its warmer weather, and the sun out so she can dry.
Spot on, the dog de flea stuff, can be used on goats. You would need to use the large dog amount though. We use it on our horses feathers, the hairy bits round the hooves, as with all that hair they tend to get harvest mites. We know they have it cos they stamp, and chew their hair on the legs. Its stops it. Also use flower of sulphur mixed to a paste, which can be got at agriculural and feed shops, that is good for fleas and irritation.
If you part the hair on your goat, and look carefully, you will see the lice. You will need to do both goats. Don't worry about you - they will only live on the goats!!!!