Engine light on after messing with relays. Did I cause a big problem?

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Was trying to diagnose why my girlfriend's radiator fan wasn't coming on. Thought the easiest way would be checking the relays. I was accidentally working with the ignition relay instead of the fan relay. I asked her to start the car while the ignition relay was out (not knowing it was this relay of course). The engine failed to start of course. Put it back in and it started. Next time she drove it the engine light came on. I really hope I didn't mess anything up. Can someone please help my sanity while we are awaiting the day we take it to the shop? Side note: The reason why I was checking out the radiator fan is because the AC hasn't been working and one of my friends (who is much more handy with cars than me) thinks the radiator fan isn't coming on.