What kind of diapers and ointment are you using? A baby of any age can have diaper rash.

If you are on antibiotics from the delivery or for any reason and you are breastfeeding, she can get small burns in her skin from it.

In normal cases, it comes down to what brand of diapers you are using and whether or not she needs to have drier skin with powder or wet skin with ointment. I don't recommend using ointment every time you change her diaper: use it only when she seems to need it. Powder isn't really even that necessary except in certain circumstances. Also, she may not tolerate the ointment you are using as well. You can try changing brands...what are you using now? Also check her wipes: she may have a sensitivity to them as well.

Every baby's skin needs a good airing out every so often. Make sure she is dry before putting on any ointment. Every few days you can let her go without a diaper on a water proof surface for a bout 5 minutes. This is very good for her skin.

Since she seems to have a rash from having moist skin (too much ointment or whatever) you can try powder for a few days and see if that helps too.

I have found that the cheaper brands of diapers all give my children rashes. I don't know exactly why: maybe it is because they are not as absorbent and don't wick the moisture away from the skin, or because of the chemicals that they use. It's a real hardship of life to buy diapers like Pampers and Huggies, but if that is what is best for the health of the baby, you have to find ways to make that work for both of you.