Mungu,
If you have an H1 and want to travel outside the US, going to Mexico and getting a visa is the best way. When you set an appointment and visit the US consulate in Mexico (anywhere near Mexico-US border), and apply for an H1 travel visa, you can use the visa to reenter the US anytime you travel outside the country, including while you travel to Nepal.
The main documents that they require from you are:
your H1 document; pay checks; work ID; official letter from your hospital stating that you work for them (may not be required, but better if you have it-will make a strong point)
proof of your academic qualifications (college transcipts)
all of your I-20's (starting from the begining)
I-94
that's all I can think of; I'm sure people will add more suggestions/advise if more things are required. But, pls consult any immigration attorney or call the USCIS service center to get accurate information. Good Luck!