OK so I helped with a paper on this a few years ago and there isn't a definitive answer as two factors greatly determine what types of radioactive materials are left after bomb detonation

First if its an air burst (most likely in a city attack) and the fireball doesn't reach the ground you get fallout entirely made up of the left over fission products from the bomb so basically the plutonium or uranium that didn't undergo fusion. This is also limited to the amount that was left by the bomb and can be spread out over a large area so may not actually, especially with uranium, be so bad as to kill you with fallout

If the bomb is a ground detonation or ver near ground you get the above but also huge amounts of contaminated dust/materials from the ground that get drawn up and made to have a short half life from neutron activation. This is way worse for you than the air burst as it can be hundreds of tons of materials its not limited to the materials in the bomb. Staying in the fallout area after a ground burst is a REALLY bad idea as your skin will get radiation burns from the outside and unless you have a good filtration mask you are going to breathe in some of the dust and this will irradiate you from the inside. Basically you dead.

If you have a large enough dose of radiation you can look to what happened to Chernobyl responders. The radiation killed their bone marrow and destroyed the cells. They have no immune system and the body begins to break down. Eventually the doctors can't even administer pain killers and you die in agony as your cells fall apart inside out. It's horrible death.