Sorry in advance for such a long post, but maybe some of this information is helpful to you...although I really hope that what I'm describing is not applicable to you!
I had a "mystery rash" about six years ago that required three trips to the dermatologist before it was correctly diagnosed. It sounds pretty close to what you described. The dermatologist first thought it might have been an allergic reaction to something, although I hadn't started using any new products at that time. On the third visit, after the "rash" kept spreading and getting itchier, something made me mention that I had just recovered from a very bad cold (or what I thought was a cold) right before the rash showed up. When she asked about the actual symptoms and what I did to treat it, I told her I had sinus congestion but primarily a very sore throat and just feeling horrible for several days. I hadn't gone to the doctor but instead took Nyquil and Dayquil nonstop the whole time. She left the room to bring in another doctor in the same building and asked him if he thought it looked "sore-ee-atic" which was not a word I recognized, so it freaked me out. Then he said it did, in fact, look like guttate psoriasis.
So all the pieces then fit together: what I previously had was strep throat, and although my body eventually recovered from the symptoms without antibiotics, the presence of the bacteria was just the trigger my body needed to flare up with psoriasis for the first time. Strep throat is apparently a very common trigger to those who have the genetic predisposition to develop psoriasis. The first flare up after this trigger tends to be classified as guttate psoriasis.
The good news was that she knew what to prescribe to clear it up at that time (an antibiotic, prednisone, a couple of steriod creams and frequent but short visits to the tanning bed!). The bad news is that once you've had a trigger, you can be fighting psoriasis for the rest of your life - as I have been. A small spot on my leg never went away after that first flare up, which I ignored since it was so small. I almost didn't notice it, but it was changing in appearance to what would be classified as plaque psoriasis (the most common kind). Maybe a couple of years later, the plaque psoriasis rapidly worsened and began spreading all over both of my legs, all over my scalp and a few isolated spots on my face, arms and torso. By that time, my old dermatologist was no longer practicing so I went to another one who tried many different treatments that did not work. I was officially classified as someone with severe psoriasis during this time since such a large percentage of my body was covered in it.
When I started a job that offered more comprehensive prescription coverage in the health insurance than what I had under my individual policy, I was able to try a very expensive medication called Soriatane. Most people opt to never try this drug since it can have many side effects, not the least of which is the certainty of birth defects if you become pregnant while taking it. In spite of the side effects I have experienced, Soriatane is the best treatment I've ever had - it has cleared me up almost completely (I say almost because a new small spot occasionally pops up that requires some cream to eliminate).
Here's hoping that what you have is either an allergic reaction that will go away completely, or "just" eczema which tends to respond better to treatment than psoriasis. Best of luck to you and hope you get better soon!