"Hey man, doctor's orders. Gotta wear it to get allergy relief. And no, can't ask about it... HIPAA stuff."
Sadly, I'm sure that will go over "not well" with ICE agents who will happily assault you for carrying a phone...
"I'll show you mine if you show me yours"
It is not a good idea to lie to an employee of the USA.
https://www.law.cornell.edu/uscode/text/18/1001