Post Contract Negotiations

What is the name of your state (only U.S. law)? NY
If a contract I signed was nonrefundable for services paid in advance but not yet totally completed, and the person I signed it with offered to refund my money for the remaining services when I asked, but then changed their mind two days later, is that the same as any other contract negotiation where you have 72 hours to change your mind? Or, can I hold them to the fact that they agreed to refund my money? I do have written proof this happened.

If you have a written offer of a refund but you did not accept it before they rescinded the offer, you have nothing.

Soon after she offered me the refund verbally, I asked her in writing when I was going to get my money back? She wrote, I'll get back to you. Two days later she wrote me an email to the effect of "sorry, I know I offered your money back but I changed my mind because the contract is clear and there are no refunds."