I also bring frozen breastmilk to the infant care when my son was there. It is the correct practise. They will follow your child's schedule to thaw the breast milk before feeding. And even if it is frozen, the milk will start to thaw in the center's fridge anyway.
I usually bring enough for my son's feeding that day.
Why are you not comfortable with them sterilising your bottles? Then how do you expect them to sterilise the bottle?