What is the feeling of 'loose/wobbly' teeth a sign of sensitive teeth?

No: It's a sign of possible periodontal disease. If your teeth are loose, then the bony support has been compromised. Make an appointment with a local dentist for an evaluation.

Gum disease : Loose teeth in the mouth is a sure sign that periodontal disease has been active for a while. If untreated the loose teeth are going to drop out of your mouth one at a time. The good news that that it is possible to stop the bacteria responsible for gum disease and to recover from having loose teeth. See your dentist for exam, x-rays and treatment. Good luck.