It is more than likely a form of dermatitis (similar to dandruff) that is caused by a bacteria. I had a similar condition, and here are a few suggestions for things to try. First, it is important that you GENTLY exfoliate (using an old toothbrush or something soft like that) no more than every other day or so for about a week. Nizoral shampoo (now available over the counter) can be used to wash your eyebrows (even your entire face!). Acne, dermatitis, and other skin ailments are all caused in some form or another by bacteria, so something chemical that GENTLY kills bacteria without stripping your skin is good. Here's another homeopathic remedy to try - plain yogurt! Works great for acne, dermatitis, even dry skin (wonderful if you have chapped lips...simply let it dry, and the dead skin comes right off with a soft wet washcloth). You simply apply about a teaspoon of the yogurt as a mask after cleansing your face (you can even add a little fresh lemon juice for extra boost), let it dry, rinse off with tepid (mildly warm) water and gently PAY your face dry (Don't rub or scrub). Don's heat the yoggurt because you'll kill the helpful microorganisms that kill the bacteria, but if its too cold straight from the fridge just let it sit out for a while. NEVER use straight rubbing alcohol on your face - if your skin is dry it makes it worse, if your skin is oily it dries it out and actually makes it produce even more oil! Try something with Salicyclic acid.
You didn't say anything about the condition of the rest of your skin. Try to really asses if your skin is really dry if you're using moisturizers (especially if its a heavy cream). Alot of people think their skin is dry when it really isn't. What's happening is they are using too harsh a cleanser, water that is too hot, not suing a toner after cleansing so the face feels "tight", not exfoliating, or not washing frequently enough. Do you use an astringeent or toner after you cleanse? That is important as well as it completes the cleansing process and removes any makeup, etc missed by your cleanser as well as any remaining cleanser, the residue of which can cause you to use a moisturizer heavier than you need which can contribute to your condition as well.
Whew! Anyway, try the above (especially Nizoral, yogurt and toner - by the way, applied with 100% cotton balls, not synthetic) and see if it works!