Car makes honking noise while driving

My boyfriend and I just bought a 2008 Honda Civic with 100k miles on it(a week ago exactly). We bought it from a reputable dealer and were told that everything was thoroughly inspected. When we bought the car they told us it needed a new break pad on one of the tires and a new engine mount and they fixed it for us.

Yesterday while I was driving home from work I heard a honking noise and thought someone was honking their horn at me. I ignored it and continued on my way home. Later that night I heard it again and realized it was coming from the car.

I've only noticed it while driving and at low speeds. It happens when I apply the brakes and sometimes when I'm pressing the gas. It only lasts about 3 seconds and stops. My boyfriend also told me that on his way to work a short time ago it happened and the gear shifter (automatic) was 'having a spasm'. I also noticed today while rolling forward slightly at a drive thru that I could hear what sounded like my front driver side tire/break making a metal screeching noise.

Does anyone know what this noise could be? Any help would be greatly appreciated.