Baby always sick since formula feeding

I've noticed a trend since I had to stop breastfeeding due to work my daughter (almost 8 months) is often sick. I feel so bad for her. She's now on formula. She recently has had constant diarrhoea followed by raw rash. Doctor advised stop formula and replace with yoghurt to see if any changes. As they say babies NEED formula at least until they're 1? Anyone not formula feed their baby (if not bf) before at age? Mother said she never formula fed us either we were fine?