It's always interesting to see what people say with a question like this, but be aware it might have no value to you. The single biggest factor is your parents, and this includes everything from finances to how strict they are to how much experience you have being away from them, etc etc.
Also, there's a lot here that's vague, and you might want to learn more before asking them. Cost is a biggie. You say you can pay your way, but do you have cost estimates? If not, you need to know the cost, because odds are high you can't.
Also, "school staff" is very vague. With many parents, if it's a teacher they know and trust, this might be different than one they've never met. But it could mean admin or other staff. The point here is few very parents would be ok sending a teen off with total strangers.
Finally, if you end up asking about this, don't use your career goal as part of the reason you want to go. Find something else, becausea nurse or even a physician doesn't need to know about healthcare systems in other countries. That's a political issue, not a medical one.