Do I qualify for FMLA Care Act Covid19 if my employer states they ran out of work, but it's not true?

I worked for a General Contracting/Construction business six months (+6 days). My son is out of school. The company gave authorization to work from home to those with children out of school. They continued to pressure me to go back to the office - I emailed and called explaining I needed to work from home because of my son with special needs needed help with school. April 6th, they furloughed a about 10 employees and told us to use our PTO and go on negative PTO. Last day was April 6th, and I emailed April 3rd that my first option was to take the FMLA 12 week paid under the Care Act. They stated I don't qualify because they suddenly ran out of work. My projects that I was key employee to are still running until mid August. They put somebody else on my place to do the work I was doing. Is there anything I can do? Is it better to let it be and take the unemployment? which one would pay more FMLA or unemployment? sorry for all the questions. Thank you in advance for all your help!