Hi, I feel so sorry for Rosie. It is so unpleasant. I adopted a Staffordshire Bull Terrier x Border Collie who suffered similar 'allergies'. Everything the vet prescribed did not work or was prohibitively expensive.
Through trial and error, we took one food stuff at a time out of his diet and quickly found out that he had ceoliac disease. We took all wheat out of his diet and he made a miraculous recovery. He lived to the ripe age of 14 having had over 6 very healthy years with us.
I hope you find a solution as easily as we did. Best wishes to you all.