I have two goats as well and get the same itchy sensation after I play with them. I can however see the little lice that are on them especially my one goat that is white. I have been told that these mites or lice are not the type that can live on humans so not to worry, but I think just being around the goats and the hay make you feel itchy. I did dust my goats but it didn't really help, it's hard to get rid of the bugs cause they live in the dirt. What did help was I used my dogs brush (the type that has really close together combs) and it pulled a lot of the lice out. You can try that. Hope that helps and let me know if you have any other advice that I can try!

for lice we use cydectin and put it down the middle of thier backs....

It sounds like you are having an allergic reaction. Possibly to something they have picked up in their coats.
You might want to bathe them good to see if that helps with your itching.

backlanelady, thanks. it never dawned on me to bathe them!

believe it or not I ocassionally spray my goats with cutter sensations (repellant). Sometimes when they are out playing they are constantly swiping themselves, jumping and you can tell whatever is crawling on them is irritating them. I spray them every couple of days and I have noticed an impovement. I am not sure if it is bad for them or not but so far I have not had any negative reactions. Oh and now I do not itch from rubbing on them.

I don't see any mites or lice on my goats,,but i always see the hens snacking on something they found on them! I'm sure it's mosquitos or something...but the hens do help keep the pests off them.