Your picture looks like an Asian eyelid. There are racial differences in the structure of the eyelids (as well as the structure of the eye i.e. angle closure glaucoma much more common in Asians and Eskimos, macular degeneration much less common in blacks, etc.)
While I cannot see the level of your left upper lid it looks like this is more skin than lid. You would need to see an oculoplastic surgeon one that is familiar with the correction of lid problems in eyes shaped like this. If the lid skin is blocking your field of vision and causing symptoms its possible your insurance might help you with surgical correction. Since this runs in your family and you have had it a long time it likely doesn't require all the diagnositic tests for things like myasthenia gravis or Horner's Syndrome in sudden onset true ptosis.