A. Since it is getting worse, you should see your Pediatrician about the rash...
From your description, it sounds like she has neonatal or baby acne. This is a common problem that begins after a baby is a few weeks old and it is probably triggered by maternal hormones before she was born.
Infants with baby acne typically get whiteheads, blackheads, and pustules on their nose, scalp, cheeks and forehead. There skin may also appear red and rough.
Although no treatment is usually required, an article in the Nelson Textbook of Pediatrics does state that 'if desired, the lesions can be treated effectively with topical tretinoin and/or benzoyl peroxide.' Since they do so often go away without any treatment, you should talk to your Pediatrician before trying something like benzoyl peroxide or Retin A (a topical tretinion medication).
Keep in mind that baby acne may not go away on its own for several months and sometimes not until a baby is six months old.
Also keep in mind that common things that parents do, like vigorous washing and scrubbing and using moisturizers and other creams and lotions, can make baby acne worse. Since it looks worse than it makes your baby feel, it is usually best to just leave it alone and understand that it will eventually go away.
Gentle cleansing with water alone, or a mild soap, is usually the best 'treatment' until your baby's acne goes away.
Infant ConstipationAs far as how often she has bowel movements, it can be normal to go 4-5 days without one, as long as she is gaining weight well and has soft BMs. If she has hard bowel movements, then she may be constipated. See this article about infants and constipation for more information.