Will taking anti inflammatory meds such as meloxicam affect testing being done for a rheumatologic disorder?

One possibility: Rheumatologic testing may include checking a blood test for the degree of inflammation that is present in your system. Common tests are the ESR or the CRP test. These might be mildly affected by Meloxicam or other anti-inflammatories, but the degree of the effect should not be enough to make or break the diagnosis, especially since there are many other tests involved.