HELP! My dog has an allergic reaction on his skin?

My dog is a shitzu, he has been sratching really hard all the time, we got him groomed and the lady said he had an allergic reaction and that we need to change his food, so we did. It has gotten worse, i now notice he has scaly, dry, flakey, itchy, scabby, bumbpy skin. and on his thighs and arms a red/ scabby rash there. My mom wont take him to the vet, but i know there is somehting wrong. HELP! P.S. He also gets ear infections alot!