Are you talking about those cheap rectangular plastic reflectors that span a few spokes and were on the bike in the shop? Trash them. I've seen the damage (and heard about more) when they slip and jam the rear wheel.

Lots of reflectors are good but not the type that cause sudden and unexpected stoppage.

Tape on your helmet can be applied tastefully and is up high where it shows.

I have reflective sidewalls also and they're probably the best for visibility and for motorists to actually be able to identify the moving object as a bicycle.