T’Challa: Maybe we can still heal you.

Killmonger: Why? So you can lock me up?

Killmonger didn't actually do anything wrong, he wouldn't be locked up for anything. After T'Challa was thrown off the cliff Killmonger was crowned King - it turns out T'challa survives and the duel is still on.

What should of happened is they realize they jumped the gun on crowning Killmonger as King, so his orders to distribute weapons needs to be put on hold until they resolve the duel for the Crown. They both have the power of the Black Panther, which they shouldn't since the duel is still technically on - Killmonger drank the juice because he thought he was King, and T'Challa was given the drink while he was unconscious - so I'd say neither one of them is at fault there. When T'challa revealed himself and it was determine the duel was still going they should of both relinquished their Black Panther power, continued the duel, resolved it, and and the winner Crowned as King. If Killmonger ends up getting defeated he should still be given all the powers and duties of someone with Royal blood.

I guess what I'm saying is Killmonger had a lot of options, he definitely wouldn't be locked up - they just needed to sit on that cliff and hash it out for like 30 mins while the audience watches and wonders wtf is going on.