You should retain a lawyer to discuss your post-conviction remedies. Many states have time limitations on when post-conviction remedies may be sought, so you should call a New York criminal defense lawyer as soon as possible.
This answer is provided for informational purposes only by an attorney licensed in the State of Delaware. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies. This answer is not intended to create, and receipt of it does not constitute, a lawyer-client relationship, and readers should not act upon it without seeking professional counsel.
I do not practice in NY, but I may offer some general advice. First, was the warrant found to violate the 4th Amendment? Unless a motion is brought to challenge the warrant and the warrant violates the 4th Amendment, these doctrines do not apply.
Your fact patterns is too confusing to determine whether the 4th Amendment was violated. Also, other facts are needed. If the warrant was for arrest and not to search a home, the address may be irrelevant. I see no reason why the warrant would be invalid because the police waited a few months to execute it. The confession may have been divorced enough from the warrant to stick, or completely voluntary and valid.
There is no way to tell if there is an ineffective assistance of counsel claim given the fact pattern described.
I agree with the first answer. You need to consult with a local, experienced criminal appeals attorney. And, you need to do so sooner rather than later. Appellate deadlines begin to run after sentencing and may occur quickly.