What is the ruling on Hajj if a woman is compelled to use perfumed soap on the Day of 'Arafah to clean her infant, and is a fidyah obligatory?

If using scented soap is out of necessity, then there is no sin upon you. However, you are required to offer a fidyah (expiation), because the prohibitions of ihram do not cease to apply due to necessity, and expiation becomes obligatory for whatever the person in ihram engages in from these prohibitions. You are required to offer one fidyah for all the times you washed yourself, and fasting three days will suffice for it. Your Hajj is valid.