PokerTracker

Can I delete the automatic notes on just one specific player?

No, that is not possible; why would you want to?

It is actually notes on my own account.

It appears to have made notes on me so everytime I start a table all the stats are at zero but there are several notes.

You can add yourself to the Ignore List then and no notes will be taken on you - you can do this via the Status page in the Tools -> NoteTracker window (the default behavior is to not take notes on hero, so you could also turn that back on, either will work).