I Just Started Meloxicam 15 Mg. This AM As Anti-inflammatory

I just started Meloxicam 15 Mg. this AM as anti-inflammatory for a slightly herniated disc injury. I'm not supposed to take aspirin with it. But I am in agony and was doing much better yesterday
aspirin.
It has been 10 hours since the Meloxicam dose. How long does it take to get it out of my system?

Please can I take at least one aspirin to get some relief.
No stomach problems.
Thank you.
Christine