Unfortunately this sounds normal to me. My beautiful daughter whom I thought was perfect started looking like a zit faced teenager around 4 weeks old. She also had cradle cap, not on her head but in her eye brows. So she had zits and crusty eyebrows. Everyone was asking me for pictures during that time I still can't let anyone see how my sweet angle looked at that time. I know she'll appreciate me holding back these photos when she's older. Although, I might use them as torture just like the dreaded naked bathtub photos when boys come calling. Just kidding ya'll!
Anyway, the acne was caused by hormones in her body. I read two schools of thought on it and one says its left over hormones from my body in hers and the others said it was her hormones balancing. Either way it will work its self out. I would just wash your daughter's face daily with mild soap and water and then I leave it alone. I liked the huggies pre-soaped wash clothes. It made it easier to wash my daughters face with soap and water without having to do the whole bath thing. It went away about a month later. There were a few days in there where it got really scaly and dry looking but it was in the healing process so it just looked worse before it got better. It also seemed to itch. She would rub her face on anything she could. I would put a really soft blanket in her hands and just let her go to town. Sometimes, when she seemed too frustrated by the itchiness I would put a mild of a lotion on her face. Lubriderm is what we used. Just imagine what you would want on your face minus any wrinkle creams. We like our children's wrinkles right where they are.
Until you get word from a doctor I would only use a cloth with warm water to wipe the eyes. From your description I can't tell if your daughter is doing what my daughter did but she had yellow scaly crud in her eyebrows. But before you try to home fix that one I would make a call to your doctor first, since you are dealing with her eyes. However, just in case they say cradle cap now you'll know there's a solution to that. For the scaly cradle cap, which can pop up anywhere on their heads, not just on their scalps, mine also had it behind her ears, I would rub a little olive oil on the effected areas and then I would let it soak for a minute. Then I would wipe it off with a warm wet cloth. The oil will loosen the flakes of skin and allow you to wipe them off without rubbing. This again can be caused by extra hormones in their bodies too. Poor things.
Its unfortunate that our sweet babies have to go through these ugly duckling phases but it will get better. Promise!