Re: Only the FDA can sell in USA
My suggestion would be that if you intend to market an FDA Class II device in the US and are uncertain about the basic requirements of the marketplace, as indicated by the question you posed, you would be best served by engaging a medical regulatory/marketing consultant with appropriate expertise to generally bring your team up to speed on such issues.
Regarding your specific question, a recognized third-party testing lab label/listing may be appropriate if your device is electrically "line-powered", or uses battery power with a significant power level. If either is the case, compliance with IEC 60601-1 (presumably to one of the US nationally-specific versions) might be either required or advisable, depending on the classification of your device. A number of other questions have to be considered in regard to marketability and regulatory compliance, i.e. who your customers will be, their local/state and insurance provider regulatory expectations, how your device will be advertised and what claims will be made, your device's intended use and risk analysis, your company's regulatory stance in other markets, the target device's presence in other markets, the general safety and effectiveness record of predicate devices in the US market, etc.