Alarm light flashing?

The other day I noticed my alarm light on dashboard started flashing when the car is shut off but still unlocked, key removed. When I lock the car with key fob and actually set alarm, the light blinks faster than usual. The light is not on when I am driving the car, but as soon as I shut it off, the (red) alarm light starts flashing within a few seconds, and as I said, the car is still unlocked. Nothing else is acting weird and no other warning lights on the dashboard are on. The car is running fine; the battery is only 1 year old. I don't know how the alarm system got triggered, if that's what happened. One other thing to note--don't know if this is important, seconds before this started, I heard a very slight flutter when I started the car. I noticed a faint yellow warning light on dashboard start to flash, then it stopped. It was very dim, and I couldn't tell what the symbol was. When I got home and shut off the car, that symbol started flashing red and I was able to find out through the owner's manual that it was/is the alarm light. (That's the only time I ever heard that slight flutter when I started the car. It hasn't happened again)