Correct me if I'm wrong, but a 300 PFT requires an 18-minute 3-mile run, correct?
If your best time ever was 22 minutes, you can forget about running an 18 in three weeks. It just won't happen.
The advice I'll give with only three weeks to prep is rather different from what I'd tell someone with three months, which is long enough to see some progress from a traditional running 5K program. But in three weeks, if starting from sedentary, you're honestly more likely to hurt yourself than make significant CV fitness gains
Run 1.5 miles every other day between now and the test. If you like, run some strides (near-sprints) afterwards, maybe 2-4 strides of 50-100 yards. That's it. Maybe some generalized conditioning like push-ups, pull-ups, and abs on the non-running days to prep for the other parts of the PFT. Same advice there: don't go too crazy on the volume, it's really too late to make great gains. You just need to prime the body a little to make use of whatever residual fitness you have.
As I said, with more time to train I wold give different advice. But if you've been most sedentary for the last year-plus, there is a much greater chance of injuring yourself by trying to cram a year's worth of exercise into three weeks than there is of radically improving your CV fitness.
I don't think I'd recommend a crash diet, either, but if you've gained some extra weight in this time, losing some of it between now and PFT day would probably be a good idea.