ID On Me bracelets
These are plastic ID capsules with an adjustable elastic band. The back says "Emergency Info Inside" and the top comes off so you can write down whatever emergency medical or contact details you want and put it inside the capsule on the included inserts or your own water resistant "paper." This way, you can change infomation yourself at any time. There are several colors with a medical emblem, as well as several colors with the "ID" logo if you just want ID for kids or other family members who might wander or not be able to identify themselves reliably or yourself, if you run or bike etc. alone. It's also inexpensive but durable.
It's not everybody's taste, but if a metal Medic Alert bracelet doesn't meet your or your child's needs, it's an option. I'm not connected with the company, but I use one and it works for me.
(relatively recent adult-onset non-ana TNA/inconclusive PA)