Guppy Lake is near the star in the above map. There are hospitals in Alpena and Tawas City. Tawas City is closest, and very easy to find -- just take US 23 south to M-55 in Tawas. Turn right on M-55 and go a few hundred yards and you're at the hospital.
Greenbush also has 911-dispatched emergency services which generally make it to Guppy Lake within ten minutes. And, of course, Guppy Lake has first aid kits on the premises.