Freelanced 1 Day on Unemployment

My question involves unemployment benefits for the state of: New York

I have been on UI for over a year. Earlier this year I worked 1 day of computer illustration from home for a company on a freelance basis. My earnings for 1 day of work were highter than the maximum of $405. At the time I tried to contact NY Dept of Labor for advice but was unable to talk to anyone on the phone. I was given (poor) advice from a fellow free-lancer not to report it as income since I wasn't "employed" by the client. However, as the year went on I felt badly about having taken UI for a week where I had earned money so I decided to take a week in December and claim that I had made more than $405 so that I would be evened-out for the year. I now received a letter asking for the name of my employer. Here are my issues:
1. This "employer" was really my client, I will receive a 1099 for my work. Do I need to report them as my employer on the letter I received? Or should this one day have been considered self-employment?
2. If I should indicate the client as the employer then the date when I actually worked will not line up with the date that I made the claim. If they contact the employer will they have to indicate the date when I actually worked?
3. If the client is not the employer, what should I do about the letter?
4. Likewise, if it was really self-employment, am I in trouble for not indicating it as such on my weekly claim?

I haven't had the guts to call UI now that I realize my mistake of not claiming it back when I actually worked. I just wanted to even out my karma but now I feel like a jerk for not having been up-front at the time. Any help would be greatly appreciated!!

I suggest again trying to speak with somebody with the Department of Labor, and to explain that it was a one-day freelance job, so you were self-employed, and to see if they require more information. I would try not to disclose too much about it, given that you've already given a false date.

You were really dumb to bring it up in the first place.

UI is NOT welfare. It is not based on income. You can have all sorts of income, so long as you are not working for an employer. A one day freelance project is NOT employment. The client is NOT an employer for UI purposes.

But now that you told them about it, deal with it. You will have to pay back the UC for that week or perhaps more.

That's exactly what I did -- the dates weren't even relevant. All I said was that I entered the wrong answer and they were able to corrreect it over the phone. However, to free-lancers on unemployment, the advice I was given was to list that you've worked a certain number of days but to consider it self-employment if you get a 1099. Lesson learned.
Thanks for your reply!