If you are interested in getting into Humanitarian work you really need to build up experience...this is what employers look for the most. This unfortunately generally means starting out volunteering somewhere for free. It would look really great on your CV to take this year (or say 6 months of it) between undergrad and postgrad to get in some volunteering/internship abroad somewhere. Pick a place that is cheap to live and its not so bad. The Middle East can be ridiculously cheap if you do it right- that's where I started out, and spent less than $200/month (and most of that was probably spent on beer when I could find it!).
You can look into internships at places like NATO, UN, etc. but they won't get you out in the field. I would suggest looking for a local NGO somewhere in the Middle East (Lebanon? Jordan? Egypt?) working in a field that interests you and setting up a volunteer placement with them. You might not have the most exciting work but you will learn about the industry and get the field cred you need to find jobs later on. Most of the serious humanitarian actors won't take you unless you have 2 years field experience no matter how much education you have. This is probably the cheapest and easiest way, you might be able to get some funding from places like the Rotary Club or Lions Club or whatever you have where you live.
Not sure what opportunities the US Government offers, but check for internships funded by them to work abroad. There are tons of young Americans doing internships paid for by somebody- they are fricken annoying because they all think they are saving the world for the few months they are abroad, but at least you get some experience for the CV- and more importantly see if you enjoy the work. Living in the middle of nowhere with no water, no electricity and only rice to eat while chaos is going on around you is not for everybody. Some of the bigger NGOs do a kind of internship/traineeship program that are good- but you would probably need your Masters first to get in.
Pretty much all aid jobs are posted here:
http://reliefweb.int/jobs so take a look and see what different qualifications they look for, you can sometimes find volunteering/internship opportunities with good organisations as well.