Hello. My name is Marc. I'm a NY-licensed attorney, and I will be happy to answer your question.
Yes - you should state the facts in an affidavit, which will be attached to your motion. But it likely won't be enough. It's up to your adversary to determine whether the facts you allege are in dispute. Your adversary will likely do this in his opposition to your motion, which will include your adversary's attorney's Affirmation stating his version of the facts. As such, without any further evidence on your part, there will be an issue of fact and your motion will be denied.
Therefore, your Affidavit must be supported with exhibits that prove your claims. If your Affidavit states, for instance, that you paid $5000 under a contract with your adversary to purchase 25 widgets, you must attach to your Affidavit the contract and related documents. If there have been depositions, you must attach the transcripts if you're citing the testimony therein. If your evidence is based on other witnesses, you must include Affidavits from those witnesses.
So yes - include an Affidavit, in which you will state your facts. Avoid the temptation to make arguments or objective statements in your Affidavit. Those go in your memo of law only. Just state the relevant facts that support your arguments and attach evidence that supports those facts.
I wish you luck with your motion! And I hope my answer helps you to better understand your issues and options. If so, please be sure to rate my answer, since that is the only way I can receive credit.