From the AIM 4-2-4:
MEDEVAC flights may include:
(a) Civilian air ambulance flights responding to medical emergencies (e.g., first call to an accident scene, carrying patients, organ donors, organs, or other urgently needed lifesaving medical material).
(b) Air carrier and air taxi flights responding to medical emergencies. The nature of these medical emergency flights usually concerns the transportation of urgently needed lifesaving medical materials or vital organs, but can include inflight medical emergencies. It is imperative that the company/pilot determine, by the nature/urgency of the specific medical cargo, if priority ATC assistance is required.
FAA Order 7110.65AA (the main document that tells ATC what to do) also identifies MEDEVAC aircraft as air ambulances:
Treat air ambulance flights as follows:
- Provide priority handling to civil air ambulance flights when the pilot, in radio transmissions, verbally
identifies the flight by stating “MEDEVAC” followed by the FAA authorized call sign or the full civil registration
letters/numbers. Good judgment must be used in each situation to facilitate the most expeditious movement of
a MEDEVAC aircraft.
Or, alternatively, as air taxis/carriers:
The letter “L” is not to be used for air carrier/air taxi MEDEVAC aircraft.
As you are not an air ambulance or an air taxi/carrier, MEDEVAC is not intended for you and is potentially confusing. It's pointless anyway- if you have a medical emergency requiring priority handling, just say that! You'll get the priority handling and you won't confuse ATC into thinking you're an ambulance.