I'm sorry you feel so uncomfortable. It sucks.
On the exercise front, you don't actually need much exercise. In fact, I wouldn't do it at all to lose weight. If you're going to exercise, don't count the calories you burn (it's negligable anyway unless you're doing a LOT of exercise), and just do it for health reasons (there are a lot of health reasons).
But to lose weight, you don't necessarily need exercise. But you'll have to be very strict about what you choose to eat. You say you count calories. Do you weigh/measure, or do you eyeball? You may be taking in a lot more calories than you need if you're eyeballing.
If you feel hungry all the time, maybe try for low calorie, high volume foods to fill you up. Lots of fruits, veggies, lean proteins, soups and stews, salads, stir fries, etc.
I'm sorry your doctor wasn't any help. They often don't get much (if any) training in nutrition and weight management, which is a shame. You might be able to ask your doctor for specific things to help you, or she/he might be able to direct you to someone else who can help (nutritionist, dietary services, etc.).
Good luck! You can do this, you know. Just do whatever it is you need to do for you.