Before I try anything else, all rashes on my children are treated with coconut oil. It is antifungal and antibacterial & many times this is more than enough for whatever is bothering them. If it persists past that I take them in. If it was a significant rash causing significant discomfort, I would go directly in, but so far we haven't had anything of that nature thankfully. The great news on coconut oil is that it's relatively cheap, available nearly everywhere, very safe for skin right from birth (barring any specific allergy) & isn't known to make anything "worse" even in the off chance it isn't helpful. It won't help bacteria grow and it won't help fungus grow.
And in case it makes you feel any better, I've been around lots of moms & babies over the years & neck rash is very common issue. All of my children seemed to have nearly no neck at all until closer to a year, so i just put oil on them daily at bedtime & that would keep it away. If I forgot, they would always get irritated, and then I would just remind myself not to miss that spot.
With an active irritation (anywhere, not just on the neck) I use a washcloth & water only. Any soaps, etc are just likely to irritate the skin in my experience. I would skip "cleansing" the area & stick to wiping it with just water & then try the oil. This is standard advice on diaper rashes & such as well when you see a doctor. The soap and any fragrance, etc is harsh on skin that is already reactive.
The link shows the findings on how coconut oil compares to other treatments on fungus.
Adding another link. This one shows how it kills bacteria too. It's a good read. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC90807/