2004 Dodge Neon - almost stalling when stopped

1. 2004 Dodge Neon SXT, 4 cyl
2. Approx. 58,500 miles
3. Automatic Transmission
4. Strange sounds - I hear a high pitched noise when the car is running, started hearing this about a month ago.
5. No fluid leaks

3 months ago - interior lights would flash at me (dash lights); check engine light/battery light came on. Dealer told me alternator was overcharging the battery. I got a code U110C - but then the check engine light never came back on. I had the alternator and battery replaced.

1 month ago - present:
Battery light occasionally comes on, but car never has issues starting.

2 weeks ago:
I had battery checked at NAPA when the battery light came on - they said it was bad. 2 days later I had it checked at the dealer - they said battery is perfectly fine. I replaced the spark plugs yesterday.

The car starts fine, but when stopped at a stop light, it idles really hard, feels like it is going to stall. Occasionally, the interior/headlights dim/get bright. I do not know what to look into next. Any suggestions would be greatly appreciated.