There is no equipment you can EDC that will safely test if the third rail is live.

I've never ridden the DC metro. In an NYC subway train, if it's safe to remain on the train your best bet is to do so until escorted off by MTA personnel or first responders. If you have no choice but to exit, if it's safe to do so head into a connecting car until you find one that's safe to wait in until MTA or first responders get you out.

If you have no choice but to exit the train, look before you leap. The third rail will be on one side of the two regular rails. Be very, very sure to not touch it.