This sounds like your flexplate and if you don't fix it the starter will get stuck on the bad spot and not start at all. I just changed my starter for a gear reduction model and now have to change the flexplate. If my new starter hits the bad spot again I am stuck. There is a guy on ebay selling them or you can get one from autozone for not much more.
I got the ebay flexplate today and it a good-to-go. There is some work on changing the flexplate, so you only want to do it once. $315 labor at a local transmission shop if I don't attempt it myself.
EDIT- When you changed your starter did you change the brace? The new starters use a different brace.
GM 15544950 - Starter Bolt
GM 14060613 - Starter Bracket Bolt - M8 x 1.25 x 20 (auto parts or hardware store)
(8mm x 1.25 bolt, 20mm long with a 13mm head)
GM 14028931 - Starter Bracket - old style Direct Drive starter
GM 23502557 - Starter Bracket - new style Gear Reduction starter
I can't believe I even have a clue what I am talking about...the forum provides all the information if you read long enough. The rest is up to you.
If i continue to use this way will it damage anything
YES