Most likely your lawyer is a criminal defense, and not an immigration, attorney.
That person needs to get an immigration attorney on your 'team'. Or, you need to have a consultation with an immigration attorney at your own expense.
SILENCE is NOT golden. You need to have court papers in your hand ... especially if your research supports your belief that it isn't an immigration conviction.
FORMER IMMIGRATION LAW PROFESSOR -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.
Since this is a case-specific inquiry, I would recommend consulting with your counsel. I would imagine that if you specifically asked re: an incident or arrest at the POE, you cannot remain silent about that, but instead must divulge the facts surrounding the case. Again, consult with your attorney.
This information is for informational and educational use only and does not establish an attorney-client relationship.