Engine light, oil light, EGR valve on 95 Grand Am GT

For about a month now, the oil light comes on while driving. At first, it would stay on for a while and then go off. Now it seems to stay on for long periods of time and sometimes does not go off until I shut the engine. The oil is full, (I change it and the filter regularly) and the oil pressure is fine according to the gauge on the dash. The other problem I've been having is with the engine light. It started coming on about a month ago. At first it would stay on for a few seconds, then a few minutes, and now, it stays on all the time. It comes on most often when I get onto the highway, under hard acceleration. Otherwise, in the city, going under 30 mph it does not always come on. Anyway, when this problem first started, my mechanic told me it needed the EGR valve. I had this replaced and the problem is till there. Is the problem with the oil light and engine light related? Any help is appreciated.
Thanks.

The oil light is controlled by the same sensor that operates the guage, and also contains a fuel pump shut off circuit. I would have the car scanned and find out what is causing the check engine light to come on, post the results, then we can go from there to help you with minimal guess work.

The oil light is NOT controlled by the same sending unit as the switch, the oil light switch is for low oil and is located in the bottom of the oil pan near the drain plug. It's pretty easy to find, just look at the bottom of the pan for 2 wires plugged into a little grime covered piece of plastic. To change this, you have to take the oil pan off the car, which can be messy. If you are confident in the amount of oil your car uses and are anal about checking your oil, you can unplug the switch, it will turn the light off, just keep a close eye on the gauge. As for the check engine light, have it scanned at autozone or any other parts store that will scan your car and get the list of codes, that will steer you in the right direction.