I have what look like mucus stuck at the top of my throat behind that thing that dangles down ?

Cold?: Do you have cold symptoms? You probably are noticing post-nasal drip which is mucous draining from the nasal passages down the throat.

Depends: First gargle with water and see if it goes away. If not, it depends on your symptoms. White spots in the throat can be "exudates" due to infection (viral or bacterial). the most important infection to check for is strep throat (bacterial), which requires treatment. If not while getting checked, your doctor can give a better idea of the cause after an exam.

Post nasal drip: That is where u would see mucous drip down from a post nasal drip. Take some warm tea with lemon and honey. It will probably remove the mucous and soothe your throat.