S.S.
Ok, first let me say that the daycare not guaranteeing that he won't get someone else's bottle is a very scary thought in the first place. I run an in-home daycare and let me tell you how fast I would get shut down if there was even a thought of another child getting someone else's cup or bottle. #1 can we say GERMS. #2 GROSS. #3 GERMS. That statement would be my first clue that my child does not belong there. There are many home daycares out there that will be able to accomodate a milk allergy, you also need to make sure that you get 2 epi-pens for your child, one set to keep at daycare and one set to keep with you.
2 of my kids have severe milk allergy and I do not have any problems keeping the milk stuff separate. If you need to bring your child's meals and snacks & drinks, that way there is no question.
Good luck to you and God Bless.