Our older dog used to break out with a similar looking rash once in a while after baths. I've since stopped using a conditioner (and always use the same shampoo), soap her up, rinse, pour a 50/50 vinegar/water mix over her (gets rid of any residue left by the shampoo), let her sit for a few seconds, then rinse again. I've also read to lather only with the grain of the hair, not in circles, as it can irritate the hair follicle and cause a rash. No more rash for her, though she does smell like a salad until she's dry :roll:
Of course, every dog is different, so no telling whether what works for my dog will work for yours, but can't hurt to try if you think it might.