"Low Oil Pressure" light being displayed while idle

I have a 2001 Monte Carlo (3.4 engine) and it has been running a little weird on me lately. It has been stalling out when idle are coming to a complete stop (not often though) This past weekend, I decided to do some maintenance on it. So I changed the oil, oil filter, transmission fluid, transmission filter, through some fuel injector cleaner in it and filled up my gas tank. The old oil that I drained out looked pretty bad, but I was barley over the 3,000 mile mark since my last oil change. Could be because I didn't change my oil filter last time I did my oil change. Anyway, after I did all that, my car started to display "Low Oil Pressure" light while at idle. (It had never displayed that before I did the oil change) I drove it around and it kept showing it when I would stop or was at idle and the car stalled out on me backing out of the driveway and when I stopped at a stop sign (it stalled out on me for the first time earlier this week when I pulled up in my driveway). A buddy of mine told me to change the oil again on run gum out engine cleaner through it to clean it out. I did, and the light was still showing. Then I changed the Oil sending unit. Still the light was being displayed when at idle or when stopped. So I didn't drive it yesterday. I drove it today but the light wasn't being displayed when I started the car up. About 5 minutes after driving it, the light finally came on for a few seconds while I was stopped at a red light but then went off and never came back on again (I drove it for about another 5 minutes) There are no strange noises coming from the engine and the car seems to run just fine, besides when it stalled out. I think my oil pump might be weak or partially clogged up. I know this is a lot of information and I apologize for that but I just need some advice. If you could please get back to me and let me know what you think, I would appreciate it. Thank you.