Yes, you would have to go back to the Confessional and confess the new sin of lying to the priest because of embarrasement. The confession is not valid if you lie to the Priest. I guess you could go to another priest if this particular priest has made you uncomfortable.

Yes, you should go to confession again, but to another priest.  Explain what happened.  Determine to accept whatever he says.  Since you are sorry enough to bring up the topic on a public forum, albeit anonymously, contrition is not the problem.  It possibly ISN'T a mortal sin because you were caught off-guard.  Let the new priest determine that.  It would be different had you spoken a premeditated lie in Confession.  Maybe your embarrassment points to your having partial rather than perfect contrition for that particular sin.

You could also simply tell the priest that you find his questions inappropriate.  You don't have to answer them.  You may have to approach a less aggressive priest for confession, but you will not have added the sin of lying.  

Before someone tells a priest they think the questions are inappropriate, I would recommend that person first look up why the reasoning behind the questions or set up an appointment with another priest to ask why such questions would be asked.

I really hope the OP has been able to correct the problem.  Good and holy Confessors are hard to find. Sometimes they have hearing and comprehension problems which can tie everything into knots.
 I strongly recommend praying a sincere Act of Contrition for starters.
Then find a different Confessor.  It is OK (laudable, even) to accuse oneself of past sins repeatedly in different Confessions.
The lie to a priest must be confessed asap.  Although something sounds strange about the whole thing.  I have had some horrible things happen in the Confessional, but we must all realize how important this Sacrament is for our salvation and do everything possible to get it done right.  Even if the priests are not how we wish they would be.