New Crown is 3 Months Old and I Can Still Feel Tooth when I Chew.

I agree with the other dentists that there could still be a chewing interference or a developing root canal problem.  I have however encountered this problem before, fortunately only a few times.  It could be that the cementation process is not sealing the tooth properly and the tooth is feeling the micromovements of the crown.  Perhaps too the crown margins are too deep and the gum area is feeling this.

When I have tried bite adjustment and the tooth tests normal for nerve health, I have removed the crown, placed a temporary crown for a period of time (2 to 3 months) to see if the symptoms subside.  If they do I will remake the crown.  If all else fails, it might be worth trying this approach.

If your crown is only sensitive for an instant after chewing there might still be interferences with your chewing cycles.  If that is the case have the dentist check for chewing interference and adjust accordingly.  If you are having discomfort or pain that appears for no reason or may persist for longer than a few seconds after drinking or eating then there is a risk that your nerve is dying.  If that is the case you will likely need a root canal.  On the average 10-15% of teeth that get crowns may need a root canal.  This does not mean that the dentist did anything wrong.  This could occur even on a tooth that did not have any discomfort prior to the crown treatment.

If you ONLY feel the tooth when you chew, it more than likely still has a spot that needs adjusting, perhaps a spot is interfering when you grind or move your jaw in exagerated movements. If the tooth is hyper sensitive to cold or even aches when you're not chewing then you may in fact have a tooth that needs a root canal,  especially if the bite feels comfortable after the bite adjustment and then feels "high" again or uncomfortable to chewing a few days later.

Good luck!