I remember my lil sidnee started with the same problem. Having red bumps and then the fur became coarse, rough and lost its shine. Then they started dropping. Initially I thought it was hot spots but my vet told me it's pimples.
Is it all over the body? Does your doggie smells (odour) soon after a bath, say after 3 days? These may be signs of skin problem. I'd suggest you watch her closely, if the fur starts dropping then you had better act fast. Since you have ruled out food, I think you should be careful of infections. Hope you can get to the root of JOJO's problem fast.
Yep, after sidnee's ordeal (she has demodex) I would definitely recommend that you take your precious to a vet a.s.a.p. But then you have to be careful - that there is no mis-diagnosis. That happened to my little sidnee.