There was a somewhat similar situation when DS was in daycare, where they mixed up the bottles and tried to give him a bottle of formula meant for another baby. They realized the mistake when he refused to drink it, and they called me at work right away to check about any potential allergies. He was about 9 months old at the time and had never had any cow's milk or formula of any kind, so I guess it's not a surprise that he wouldn't drink it. Then they said that unless it was okay to give him formula, I would need to pick him up because they didn't have any other bottles to give him. That's when I realized that my pumped milk must have already gone to the formula-fed baby!
I picked him up and he was fine, and no one asked me to take any blood tests or anything like that. I can only assume they told the other mother what happened but they never told me which baby got my milk. I really didn't mind except that it was a sloppy mistake (how can you mistake EBM for formula?) and we switched daycare centers shortly after that.