First, see if you can find out what the exact error code is that is associated with the check engine light. The format is “P1234” - post it. If your mechanic doesn’t have it and the light is on large chain-type auto parts stores will read these for free.
Second, it may be that you are misunderstanding you mechanic. But if not then you surely need a new one. There is absolutely no way whatsoever that changing spark plugs is going to address a problem of running too rich. This condition will occur from the engine either getting too much fuel (e.g. malfunctioning fuel pressure regulator or injector problems) or not enough air (e.g. old dirty air filter). It can also come from the engine thinking that there is too much fuel or air (e.g. bad or dirty mass airflow sensor). It cannot be caused by bad spark plugs.
Third, even though I can’t tell from your description whether you’re having a transmission or engine problem, you absolutely should know how to check your transmission fluid. The procedure is described in the owner’s manual. Basically, the car should be at full operating temp & idling in park (sometimes neutral) on level ground. You pull the dipstick, wipe it, insert it fully and pull it - there are markers that show the proper level. It should be nice and red - brown is bad; black is terrible. It should just have a mild “oily” kind of smell - nothing strong or pungent or burnt.