2002 Toyota Corolla Beeping and accelerating noises

I purchased a used 2002 toyota corolla, that at the time had 24,000 miles. I now have 200K+ miles and have done due diligence in terms of regular oil chances, brakes, alignment etc. Lately my car has been making a beeping noise, three or four beeps in a row, usually at stop signs or sometimes when I am driving. Also, when I accelerate I hear a loud shoveling noise that seems to be coming from my air conditioning. It only makes that noise when I accelerate really fast or when i'm idle and about to accelerate. My father has taken this car into the mechanic, and was told that this model doesn't have a timing belt. Any suggestions?