These matters are governed mostly by state law so you need to consult a local attorney in New York. With that said, non-competes are often very difficult to the employer to enforce, and where enforceable, usually involve their existing clients (who may be deemed as part of "trade secrets") and non-solicitation wording. It appears that it is the non-disclosure that is most at issue in your matter. The wording of that provision in your agreement should be looked at carefully, as the usual provision states that information already in the public domain is published and thereby deemed non-confidential. Companies generally like privacy. With that said, few companies pursue action in this type of instance unless it is on a new product/innovation (but don't rely upon that). What you might do is write a letter to the company asserting that you don't believe the provision is enforceable, but nonetheless desire to respect their wishes as a former client and would like to know how and under what circumstances that you can reveal the work you have done for them. Be persistent if this is important to you, but be courteous and professional at the same time (if you want to get the response you desire).
Confidentiality and "non-compete" agreements are quite common in New York, and courts will uphold them if reasonable in scope. It is important to consult with a New York lawyer with expertise in this area so that he can focus on the specific language in the agreement that you signed. Further, you need to discuss with your lawyer the precise details about the nature of your job, the work you created, and the extent to which your former employer could reasonably expect you to maintain confidentiality. The attorney-client privilerge permits you to disclose this information to your lawyer so that he can advse you properly concerning your legl rights and obligations.
In general, when you are paid by your employer to create, design or write something, you create a "work for hire" that is owned by your employer. Your employer owns the intellectual property rights arising from works that you create while being paid by your employer. It is often critical to maintain confidentiality in order to preserve your employer's right to exploit these intellectual property rights. Thus, employers have a legitimate basis for expecting you to maintain confidentiality regarding the work that you design.
Further, New York courts also will uphold the legality of agreements forbidding you from competing with your employer for some reasonable period of time after termination of your employment relationship. Courts have been particularly willing to uphold limitations on dissemination of client and customer lists. Courts have also upheld geographic limitations, if reasonably limited in scope and time.
On the other hand, you are correct that confidentiality and non-compete agreements are sometimes overbroad and unfair. Courts generally are loathe to uphold such agreements if they would totally prevent you from earning a living in your chosen profession. Such agreements may also be deemed unreasonably broad if they extend for an unreasonable period of time. Thus, most employers realize that it would be legally problematic for them to prevent you from obtaining another job in your chosen profession. Further, most employers understand that you should be permitted to reasonably display your past work so as to establish your credentials to potential clients and employers.
As a practical matter, whenever a client comes to me with this type of problem, I advise them to try to work this out in negotiations with their former employer. In most cases, a letter from your lawyer to your former employer will lead to a satisfactory negotiated solution. Your former employer will usually understand that it could face significant and unnecessary legal expense if this issue is not resolved amicably. And there is usually a way to accomodate the interests of the employer and former employee in a reasonable manner.
Where the economic stakes are high, it can become difficult to reach a negotiated solution. Thus, there are cicumstances where it is necessary to ask a court to resolve the parties' dispute concerning the fair and reasonable scope of confidentiality/non-compete agreements. Keep in mind that many such agreements mandate that disputes that arise under the agreement must be submitted to arbitration rather than courts of law. Whether the issue is presented to a court or an arbitration panel, there is a large body of case law concerning these issues which will guide the decision-maker. The possibilty that the dispute might have to be resolved in court (or in an arbitration) provides additional leverage that, in most cases, will lead to a negotiated settlement.
The most important thing to remember is this--there is no "one size fits all" solution to a matter such as this. You need to retain a lawyer to review the agreement at issue and the specific facts and circumstances of your case. You then should work with your lawyer to develop a strategy for resolving the issue.
Much more information is required for a comprehensive answer, but it sounds like the agreement could be found unenforceable by a court. Non-compete agreements cannot be overlybroad in either geographical scope or time, with some exceptions. if they are, they can be voided.