If you make contributions to the unemployment tax then you can, if you don't then most likely no.
If You Were Self-employed, Can You Still Collect Unemployment?
Unemployment benefits are benefits that are paid into by a employer,did you pay into unemployment,If you did I would think you would qualify if not there is nothing for you to draw,but check your question with the unemployment Dept in your state, but normally that is how it works you must pay into it to draw from it...hope this helps