There are two kinds of tests that are done (presuming you can't get a bulk sample of the "stuff"). One involves monitoring the air to see if enough particulates(dust, etc.) are present that exceeds a value, such as 1 part per cubic centimeter.
If so, you would need to then have the particles analyzed by a microscopic test to see what they are.
Having a clear conscience is sometimes worth the money. The above tests should eliminate all doubt.
Any reputable environmental Co. could help. Although OSHA doesn't get into residential "stuff", calling them can lead to some reputable companies in your area.
I understand your concern is fibers in the carpet. Vac with a hepa vac, clean the carpet with steam, and hepa vac when finished if you wish. I sincerely doubt you would find any fibers after that.