We changed Bethanie's milk and didn't notice anything major, although she was a few weeks older. New babies nappies will always be a bit runny as im sure you've noticed, but so would ours be if our diet was milk alone. If it's really runny like that, it probably is the milk, but if it doesn't improve.. id take her to see a doctor just to be 100% sure.
Hope it passes.. for both of you lol.