Yes, you could cause permanent damage. Any numbness or tingling that doesn't quickly resolve itself after a ride is cause for concern. One way or another, you are compressing a nerve. It could be as simple as the tilt of your bars, or you weight could be too far forward. If you haven't had a professional fitting, I'd start there. If you have,go back for another evaluation.

I rode for less than a year on a bike that induced bad hand pain. My hands have never been the same. So please take it seriously. One word of caution about heavy padding on either gloves or bar tape. For some, it acts as a solution; for others it makes it worse.