Hi, thanks for using healthcare magic
The white rash on her tongue sounds like fungal infection
as does the rash around her diaper area.
The diaper rash
would require topical antifungal
creams , combined with a mild steroid cream. The oral rash would be treated with an oral antifungal
The oral candidiasis
(fungal rash) is commonly seen in children especially when their immune system is down which is the case with your daughter.
The cough is likely part of the progression of her illness, a cough suppressant would help, if it is wet, she may need something to help breakup the mucus.
You can consult your doctor regarding the rash, he or she can also show you methods to ensure that she receives the appropriate medication.
I hope this helps