Generally an ER won't do a Mri on a sprain unless they think
it's needed. You can't just ask. They must code it for Ins. co.
to get reimbersed. If it doesn't match need, they won't get
paid. It might be considered un-necessary testing & they might
say you insisted no matter who paid. A general xray is ususal
for ankle sprains but up to Dr's decretion. Use ice & loose
ace-bandage & see your own MD. Crutches might help & keep
elevated. The fastest exam if no family MD would be urgent care
to evaluate. They contract cheaper than hospital fees. Ibuprofen
may help. Gd-luck.
If you have insurance, your co-pay would probably be the same at either location. Of course you could verify this by calling both places or checking with your insurance company.
Good luck with your MRI !