What could cause an itchy rash all over with bumps. This is for a 27 yrs male, otherwise well, no allergies, takes no meds?

Many possibilities. A rash such as the one you described could be contact/irritant dermatitis (reaction to something in your environment like soap), viral illness, idiopathic urticaria (hives). I would recommend seeing your doctor for a definitive diagnosis.
Hard question . This is hard to answer from your description without an image of the rash. It can be pityriasis rosea, particularly if one of the patches started sooner and is larger than the rest. Guttate psoriasis may also be a culprit, particularly if u recently had a sore throat. Also may be lichen planus. See a doctor to get a more accurate diagnosis.