What should I do about a receptacle with 2 circuits going through it where white wires are hot?
Is it OK? No. Aside from the dangerous confusion you experienced there is an ongoing safety problem here. You have hots from two circuits going into one receptacle, but you only have one neutral. By placing load from two circuits onto one neutral wire, you have the risk of overloading that wire without tripping the circuit breakers for either circuit.

It's possible to safely have two circuits feeding one receptacle, if you have a hot/neutral pair for each segment. Additionally, current code requires dipole breakers in this case, so overload on either circuit shuts off both.

To fix this, you need to determine which hot is associated with the same cable back to your circuit breaker as your effective neutral, and disconnect the other hot. (One of the black wires may be feeding another receptacle; make sure that receptacle has a correct neutral.) You should also trace the cables to adjacent receptacles/junctions and check those -- this isn't a good sign about the quality of electrical work in your home. If you're lucky, the fix is just a matter of a few changes in receptacle boxes. If you're unlucky... well, it's better to find out through inspection than through a fire.

You'll want to get a non-contact voltage tester. Be safe!