Many product types are subject to multiple regulatory requirements in USA. Some medical devices are also PPE, and subject to regulation by OSHA. Some devices, and also some pharmaceuticals, are also subject to regulation by EPA.
I can easily envision that a multiple use garment for wear in a medical setting, not particularly distinguishable in concept from garments for wear in some other work setting, might be considered to be subject to the various garment regulations promulgated by other federal and state regulators.
On the other hand, the most commonly applicable garment labeling regulation per your original question would be the FTC's "Textile Products Identification Act", 15 USC 70. The TPIA states it's applicable to "household textile articles", which it defines to mean "articles of wearing apparel (...) of a type customarily used in a household regardless of where used in fact." In other words, work garments are covered. But, TPIA section J part (a)(8) excludes "(...) other textile fiber products, the labeling of which is subject to the requirements of the Federal Food, Drug and Cosmetic Act of 1938, as amended". Thus if your product is clearly a medical device, and is only marketed as such, it's not covered by TPIA.
Or, of course, it might be exempted from TPIA if its design and functional nature are so specific to a medical purpose that there's no way it could be interpreted as "wearing apparel" in a garment sense. That however is a difficult boundary, in that I've seen broken-arm slings considered to be wearing apparel.
I don't know about other regulations, especially at the state level, though. You'd have to do more research. A lot of regulatory legislation has been passed over the years pertaining to garment manufacturing and marketing.