What are my rights if today my employer demanded that I give my phone up for the rest of my shift?

Your supervisor is allowed to require employees to give up their phones at work this is perfectly legal. It is also perfectly legal--and, in fact, fairly common--for lower level employees to be treated differently and worse than supervisors. There is nothing legally objectionable about what you describe.

Unfortunately, you probably have no rights here. The fact is that an employer can set the terms and conditions of employment much as it sees fit this includes who can and can't carry cell phones. For your part, you can comply with your employer's mandate, quit or face termination. 
The exceptions to the above are if this action violates company policy or the terms of an employment contract, union agreement or the like.
Additionally, if this treatment constitutes some form of legally actionable discrimination or retaliation, then it is illegal. However, not all discrimination is unlawful, therefore, not all employees need be treated the same or even fairly. Discrimination is only actionable if it comes about as a result of an employee being a member of a "protected class". This means that if you were prohibited from carrying a cell phone due to your nationality, race, religion, gender, sexual orientation, age or disability, then this prohibition would give rise to a legal claim.
Further,