Welcome to the BA section of FlyerTalk,
amoghthegamer, please make yourself at home. We all started travelling at some point in life, though it can be addictive, so please stick around and tell us how you get on. The other members of this forum will no doubt be very generous with their time in answering your questions, and there is also a team of ambassadors out there too. Can I be nosey and ask what is the subject of the essay?
Now there are a few points to make. Firstly your breakdown above is one way only, so you can double that for the return ticket. The second thing is that you also need to add in taxes, fees and surcharges on the flights. Getting to ORD won't be too bad, but from ORD to HYD you need to add in approx $800 for that on top of what you have put above. Consequently using Avios in this situation is poor value in my view. Thirdly, it's not a direct flight from ORD, you will have to change planes at LHR. Finally availability during the Olympic Games is not good. You may get availability at very short notice (there seems to be some for the next few days) but otherwise at this late stage I think you will strugge.
This is a good thread if you have not seen it already.
Now I've visited all the countries in your list. I think they all have considerable charm and attraction. I agree Haiti is an acquired taste! Costa Rica, however, is somewhere great, and you would be able to get there via AA relatively cheaply.