Good answers. You are safe to make the trip to your parents’ mechanic. The dreaded CHECK ENGINE light mostly relates only to emissions. The oil light and the temperature gauge are far more important. Unless, as Cigroller says, the same CE light starts flashing, you’re okay. If it does, pull over, turn it off and call AAA. Which you should get if you don’t have it.
But first, on the way to the parental mechanic, if there is an Autozone near you, go there first and ask them to check the code for you. The chain has recently updated its diagnostic capability and might be able pinpoint the exact repair. It helps a lot if you know what you want a mechanic to fix and get a price to fix it up front. GL.