In general, almost all noses are numb right after a rhinoplasty. In most cases its the tip that is numb, but this numbness can extend down to the upper lip, and in rare cases some of the teeth. There are nerves that are cut and stretched during a rhinoplasty, and it takes a long time for those...
I think you might want a clarification. I suggest nose exercises for my patients, but you need to be clear what that means. One, I agree that you should not manipulate the tip of your nose at all. That has been surgically corrected, and could be disrupted with aggressive...
It can take several weeks for the initial swelling to occur, then months for it to subside. Swelling in the tip generally takes the longest to subside, and it's generally this that is causing the hardness you're feeling. Please wait a few months before evaluating your results. Best of luck!