Why did me ETS off light come on simultaneously with my check engine light?

While driving this weekend, my ets off and check engine light came on. Also, my oil change light comes on, then goes off sporadically. I took it to Auto Zone, and they told me it could be my transmission. My car is running fine, it shifts good and the light went off as well. Should I be worried about my 96 Chevy Cavalier, or should I ride it out?