We had similar problem years ago when i first moved into the house ( our first house, first winter ...)
Didnt know much bout ordering oil ( when, how, how often ...), and sure enough , ran out of Oil on a friday afternoon during a huge snow storm. couldnt get a delivery until monday. Spent all weekend with me, my wife, the kids and 4 cats locked up in the smallest room of the house, with an electric heater, and air-blow popcorn maker , and what ever blankets we could find.
Going to the bathroom was a real treat ( that seat was very coooooooold) And breathing outside of this little room you saw the 'smoke' coming from your mouth in every breath ( very strange to see this happen inside your home)
Anyway, we got through it, pipes didnt burst, no one got sick, got our oil, and nver made the same mistake again...
Luckily our boiler has been functioning ok , but i can definitely empathize with how u feel now. Hopefully it is a simple , quick fix...
How far up north in maine are you ??