New Born Having Loose Bowel Movements , Rash Over Body, Dry Skin After Using Formula Feed. How Long Will It Take To Subside?

Hi there. My daughter is 5 weeks old and experiencing allergy type symptoms to the formula we are using. I stopped breastfeeding at 3 weeks due to her constantly power chucking after every feed and frenzy feeding . I put her on s-26 infant gold formula and she was still power chucking. Her other symptoms include: bowel movements loose/watery, restless, gassy, rash all over face and upper trunk, dry skin round ears and forehead , fussiness during feeds, refusing feeds, constantly hungry. Yesterday I changed her formula to a soy one, her face rash appeared to be clearer today- aside from when she gets irritated then it looks like it flares up, she has just done a poo which seemed to be very painful for her and it was half hard green half watery yellow. She seems happier, I am just concerned she may also be reacting to the soy. How long will it take her rash etc to disappear, and how do I know if shes sensitive to soy also? (Note: Her 3 year old sister was sensitive to dairy and has a moderate allergy to peanuts) Thank you for your help.