I was mowing my lawn and I ran over a huge tree root and I heard a very loud noise and it turned off. I turned it over and saw that some of the oil spilled over. Could this mean I blew my engine?

Best case, no damage.

Or the flywheel pin sheered like it's supposed to.

Disconnect the spark plug and try to move the blade by hand or if it has a re-coil starter try pulling it slowly and check for any binding.

If the flywheel key is shot then the engine will not start because it's out of time.

The blade could also have gotten bent in the process.

Once you do the above tests, you can try to start the mower. The mower can be difficult to start when the mower has been tipped on it's side.