I looked at the pictures. They don't look like cold sores, no. The technical term for the area on your lip is leukoplakia (white patch) but why it is there, I don't know. If it continues to be present, I would go to see your dentist for a further evaluation. Stop trying to remove it with a toothbrush, you will be confusing the picture for the dental evaluation.
If the area changes or becomes a blister, then I would be concerned about cold sores. If that happens, get seen right away for treatment.
it never became blister. But its still there. Not as hard and prominent but patch is still visible. Is this something to get worried about ?? should i visit dermatologist for this ??
If the patch remains for a few more weeks, I would have it checked out, yes.