OK glad to hear that you are concerned about the potential consequences.
1. Yes the machine needs to be inspected as all the Pilots here have correctly alluded to. Dont be shy of Engineers they are there to keep you alive & the machine making money. So build rapport with them.
2. machine is grounded, so DON'T fly till engineer clears the machine.
3. there should not be any delay in reporting this exceedance to the CFI, AME etc. Don't wait a day or 2, it should have been done same day. Even if it was the last flight of the day & everyone had gone home that Instructor should have called his CFI? If not get another Instructor.
4. Avoiding ANR? My friend that is rubbish. Apart from the fact that ANR will save your hearing so that at age 70 you'll still hear your wife nagging you. More importantly you will hear more things going on with both engine & all rotating bits. ie; few years ago I heard of a CPL doing a check ride wearing ANR, the old timer & superbly qualified senior Instructor scalding him over ANR when the CPL said, 'can you hear that strange graunching noise? The old Instructor said 'NO' everything sounds fine? But he proceeded to do an precautionary landing against advice of the Instructor only to discover that the hydraulic pump was destroying itself on a AS350 dumping hydraulic oil overboard & they were seconds away from losing all hydraulics, but saved by the refined sound inputs heard through the ANR there was no dramas.
ANR will help you greatly hear odd things that should not be there. As for not hearing the engine, that's crap, when you lose the engine the massive yaw will let you know when power is gone before the noise stops (engine failure). So get ANR & save your hearing & be able to hear all the noises, both good & bad. Also reduces fatigue hence you stay sharper longer
VF