Looking into other countries is wise. And if you certainly want to study outside of Mongolia, I would encourage you to also look for countries that might have cooperative arrangements with Mongolia. In India, which has excellent English language universities, and some of which include a number of international students (like Delhi University), I believe that they still give preference to students from South Asia, but I’m not sure about how that would work with Mongolia.
Of course - give the US colleges a shot - but you can’t count on them giving both admission and sufficient financial aid.