2003 Saturn L200

Recently I noticed that after driving for a while then turning my car off the fan wouldn't automatically kick on like usual. Then I noticed the temperature gauge went a little higher than normal but the car was not overheating. Last night after driving on the freeway and almost home, I noticed a humming sound from the front of the car. I pulled into the driveway the humming became louder so put the car in park, popped the hood and it was dark I couldn't see anything but it sounded like a high pressure blower. I turned off me car and the sound whined down. This morning I went to start my car and immediately was that sound again. I popped the hood and looked around, didn't see anything unusual but felt air coming where the fan is but it didn't look like it was even moving! I'm worried it may be the alternator. Any thoughts or advice? I'd appreciate it. Thank you.