Hello and hope you are doing well.
The rash could be due to the infection. It could also be purpura due to the low platelet count. Sometimes the rash could be due to contact dermatitis, that is exposure to an irritant like a chemical or metal or anything you are allergic to, it can cause rash. But to exactly pin point the pathology you will need to consult your primary care physician who will examine you and may ask for more blood tests. If the need arises he may refer you to a dermatologist.
Hope this helped and do keep us posted.