My seven week home bred chi/poodle had large red looking veins under eye lids. I have noticed same in my own eyes. They will move when pressure is applied bit I dont know if thats just from surrounding fluid makes them do that. Neither adult dog/parents have it. Could there be a cross species parasite that it could be?
To be honest with you -I don't know what this is. My advice is to take her to the vet to be checked. The vet will surely know if a cross-species infection is possible, and if so, consult your doctor too.