Get a degree.
I made the mistake of thinking that US Army Fixed Wing flight training would make up for the difference in not having a degree.
Wrong. It took me 14 years to get a good flying job. You can fly, and I did, Twin Otters, Shorts, Fokkers, but like me don't plan on making any money until you get a degree.
Plus if you are furloughed, a degree might help you feed yourself and your family.
The only plus side of going to flight school first is that you *might* be able to pay for your college while you go to school.