My
DS was the same when we started at daycare, but they managed to get him to sleep - he basically konked out in their arms. He didn't go for long cause he kept getting sick so never really settled in properly or slept well there, but my
DH, mum, and babysitters were all able to get him to sleep without the boob.
Not sure if someone else suggested this, but at his age you could just try a sippy cup for EBM, if he's not keen on a bottle.
DS started using a teddy when he started at daycare too.
good luck
ETA - don't be embarrassed about being his lovely!