Nursing on shabbat

Question

Re: Using a breast pump on shabbat -- My wife feeds our 2-week old newborn by nursing, most of the time. She has alternated with formula as well. However, in the last few days, she has noticed that when she feeds the baby using formula, the baby does not tolerate it ( he spits it all up ). Also, from nursing the baby, she now has a sore on one side and cannot nurse from that side. Instead she feeds the baby from the other side ( directly ), and pumps from the sore side -- and that milk is then poured into a bottle to bottlefeed him. The baby needs the qty of milk from both at each feeding. May she use the pump on shabbat in such a scenario ? Thank you.