Hello Kaif and welcome to the board.
You have brought up some good points, but until you have a DEXA scan you can't know if you have osteoporosis or not. The only way to tell if your bones are losing density/thinning is for a radiologist to look at the scan and make that determination. Osteo doesn't have any outward signs, it happens inside your body. Could it be that your hands look thinner because you have lost weight from your diet? From what i have read even with osteo the bones stay the same size, only their density is reduced, not the size. If osteo caused people to be thin many of us wouldn't be trying to lose weight. I am not trying to lessen your concerns, but to my knowledge it doesn't work that way unless there are other causes for the weight loss. Being thin is risk factor for osteo and so does family history, but neither of your parents have it.
Walking is a good example of weight bearing exercise and something you do everyday. You could to talk to your dr. about what kinds of exercise you can safely do with your existing back and wrist problems.
Since this is a concern to you maybe you could talk to another dr. who will recommend a DEXA and also look for other causes. Good luck. take care...phyllis