It's sounds like Seborrhea (AKA Seborrheic Dermatitis or "Cradle Cap" in little ones) and is a step up from dandruff but not as bas as eczema. I've had it since junior high school and have it worse around my hairline, the sides of my nose and a little in my eyebrows. Mine can itch and hurt when I don't treat it, so it probably does hurt her some. In fact, before I knew what it was when I was young, it would get so bad and I would pick off the flakes until it would bleed. No fun.
Get Head & Shoulders Sensitive (just don't get it in her eyes). That is what finally cleared up my daughter's cradle cap (per her doctor's suggestion). I have to use a stronger shampoo, Nizoral, but I think H&S should be fine for her. Wash her hair every-other day at first (both washing too much and not enough will affect the oils on her scalp and make it worse) and use the H&S each time. Once it's better, just use it once a week as maintenance. Just make sure not to pick at the flakes - that will just make it worse and raw.
Another thing you can use is hydrocortisone cream ($1-2 at any drug store). BUT, I would check with her doctor before using it. It is a steroid cream and is great for flare ups, but steroids makes you skin thinner and you only want to use it sparingly (and it might be too harsh for a toddler's skin).
I'm not sure if the brown spot is related or just a mole or freckle. I would have her doctor look at it at her next check-up just to be sure. If the H&S doesn't work, it might be eczema and you should talk to her doctor anyways. Start with the H&S and then go from there. I'm guessing it will clear it up. :-)