Car Starts but won't stay running!

I have a 2013 Toyota Corolla with approximately
92,655 miles. I had gotten an oil change at Walmart
and about 3 days later my oil light came on and my
car stalls and dies on the side of the road. I couldn't
get the car to turn over or anything. I used a code
reader and got p0012/p0014 with shows Bank 1. I
tow it to a shop where they say I need to replace
my entire engine that'll run me for 3,500. I get it
towed back home where I noticed my mileage was
over the amount my service contract I purchased
through my auto finance. So out of pure curiousity I
decided to try and turn my car on. This time it starts
up and ran for about 20 seconds as I kept my foot
on the gas revving it up. As soon as I released my
foot the car cut off. It finally started after leaving it
for a couple days after a fail. What could be the
problem? I really don't want to drop all that money
on a car I am still making payments on that could
be fixed for cheaper.