The first world doesn't help the third. We don't help, we exploit. Not as brutal as in colonial days, today it's more subtle: Closing our borders for agricultural products so a couple of American sugar farmers can have a good living is just one of many examples. Same with rice, meat, just about every agricultural product is protected by taxes in the western civ, while we demand from the developing countries that they open their borders for our services and technological products. There's a good reason why Brazil, India and some African countries brought down the newest round of the World Trading Organization talks.
About sending doctors: Screw that. Screw that big time. In fact what happens right now is that America, Britain, Canada and to a lesser extent other countries of the western civilization are actually draining medical personnel from developing countries such as Ghana and Malawi. There are more Ghanese nurses working outside of Ghana than there are in Ghana, same with Malawian doctors.
Umm, now i could say that the people and the country get the politicians they elected (or deserve), but that would be cheap. It's still true, though.