Why is my dog itching so much lately?

I just got a new addition to the family. A australian shepherd mix. I just got him last sunday on fathers day. I had him on purina pro plan and just switched his food to blue buffalo puppy mix chicken and brown rice. I am also giving him a couple of baths using a shampoo by Natures Miracle coat enhancing formula. He is itching the last couple days like crazy and chewing everywhere. He is also sneezing with alot of snot coming out shooting snot everywhere its kinda nasty lol.