Ouch that sounds painful.
It sounds like you are doing everything you can. If you start to see any pus or yellow fluid oozing from it, get it seen by a doctor.
I wouldn't recommend taking the nail polish off right now, unless you can figure out a way to do it without the nail polish remover getting on the cut. That would HURT.
I don't know where you are traveling, but is there an urgent care or anything nearby? You may not need to see them, but they might be able to help figure out what's under the nail, or give you an antibiotic cream to put on it. It's also good to know it's there in case it gets infected.
I hope you feel better. It just really sounds painful. :(