
Hi,
Allergies don't only show up as skin related problems but can manifest themselves as gut problems such as sickness and more commonly loose, runny or mucus coated poos :(
Any dog as with people can be allergic to virtually any ingredient. Try and stick to a simple diet (needs about 1 months trial) by a well known quality make, eg. James Wellbeloved. I'd try their Turkey & Rice diet - this is fairly bland, doesn't contain many of the cereals etc that dogs are commonly allergic to either. A lot of dog foods are chicken or lamb based which, along with many grains, gluten, cereals etc can be catalysts for GI problems so turkey is a slightly safer bet first hand.
Specific allergy tests can be done by your vet. What makes you think your dog has an allergy? Whatever the symptoms, I think I'd visit the vet first to get a professional opinion in case you are treating something with diet only that really needs medication.
Good luck, Teri :)