Tooth sensitivity usually occurs when the softer part of your tooth called 'dentine' is exposed due to the erosion of the enamel. I'm sure your dentist must've looked into that part but to be on the safer side, try using a toothpaste that fights tooth sensitivity and lets hope the issue is resolved without extraction.
I think the problem is with your wisdom teeth. The wisdom teeth might be pushing all of your teeth in due to its growing sideways. This is causing a block and nerve damage. This ight has caused you a feel of sensitivity. Get your wisdom teeth removed.
I'm not quite sure why the wisdom teeth are causing the sensitivity to sweets. They may cause some pain or discomfort such as a sense of pressure but if they aren't out yet, it seems unusual to me.
Can you get a second opinion?