Driver's side headlights went out

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Power for the headlights passes through the switch as one, so if the headlight switch were bad, both headlights would have been affected.

The problem can only be in the wiring, fuse, connection or headlight if the other is working.

Try swapping the bulbs between the passenger and drivers side. If no change, swap them back to their original headlights, then swap ballasts. This will tell you if it's one of the two.

Also, if the connector is loose like you said, you need to fix that as its a common issue that can cause the symptoms you describe.