Don't know if you're doing a combo of breastfeeding and formula or if your baby is on formula only, but either way, that rash you're describing is a HUGE tip-off that there's likely some allergy going on. With my son, we thought the same things... oh, a little rash, maybe baby acne, maybe it's just that it is dry and winter, etc. -- but then it got to the point where, when he was only 4 weeks old, his face just WASN'T getting better. It was SOOOO red and dry, and he was rubbing his poor little cheeks back and forth on our shoulders as we held him (because his little cheeks itched so badly). Ugh, it was awful... his sleep was terrible, he seemed crampy and his poops were gassy, smelly, and mucousy. And he was 100% breastfed, too!
Turns out for my son that these symptoms were an allergy to BOTH cow's milk protein and soy protein - as soon as I stopped eating those (and therefore no more of that in my breastmilk for him to get!), his sweet face cleared up and became so smooth and soft, his poops became normal breastfed baby poops, and his sleep GREATLY improved. He was just overall a MUCH happier baby.
Here's some good information that applies to formula-fed babies as well as breastfed babies:
http://www.kellymom.com/babyconcerns/food-sensitivity.html
And I wouldn't "wait 6 months" or anything crazy like that - if your baby is having a bad reaction to their food, and you switch to something else, you SHOULD see some serious changes within 1-2 weeks. If NOT, then I'd be asking for hypoallergenic formula (if giving formula) or I'd be eliminating the most allergenic foods from my own diet (if breastfeeding).
Last but not least, if you are breastfeeding but supplementing with formula due to weight gain issues, *please* know that there are OTHER WAYS of getting more calories to your baby *without* using formula (if you're breastfeeding + giving formula, simply removing the formula AND replacing that supplement with pumped breastmilk, *that alone* could solve the allergy problem!). You can rent an electric breastpump (or buy a manual breastpump) for cheaper than the cost of formula, and instead you can pump your own breastmilk and feed it by bottle to your baby. No need for formula, and no need to mess with your supply (giving formula and NOT pumping is very likely to mean a decrease in your milk supply, and it could possibly ruin your breastfeeding relationship UNLESS you are really being strict about pumping each time you give formula). If you are interested in continuing to breastfeed, and you want help with figuring out how to keep up your supply and wean off the formula while still getting your baby all the calories she needs, contact your local LLL leader - they're volunteer moms who have breastfed their own babies, they're FREE, and most of the LLL leaders and the moms I've met at the meetings have been really nice. If you talk to a leader that you don't really like, CALL A DIFFERENT LEADER! :) Here are some contact #s for your area:
http://www.lllohio.org/groups/toledo.html
Best of luck - I hope you are able to find out what's bothering your new daughter ASAP!