If you have not had the drivebelts replaced in the last 30K miles or 2 years or if they look at all shiny (glazed) or show an extreme number of tiny cracks over its length, then I would say it would most likely be a slipping drivebelt or bad pulley bearing. I would highly recommend against any belt lubricant spray. The sprays are a temporary solution at best, and some cases, will significantly weaken the belt.
You will need to isolate the sound - will be difficult, since the squealing seems to be load driven (vehicle in gear, accelerating from a stop). You can try and duplicate the sound by brake torqueing the vehicle and see if the noise starts up. Basically, you have someone view the drivebelts with the engine running, hood up - set parking brake and firmly hold down the brake pedal as you shift into drive - maintaining brake pedal pressure, depress the accelerator to raise the engine load - done relatively quickly, no harm will be done to the car - make sure to give the transaxle time to cool down. This will have the same effect as towing a trailer uphill.
You should note squealing right away - if it is a load driven issue. If you are able to - have a squirt bottle handy with some plain water inside. Liberally squirt the belts with water (may be easier to do this with the engine off), repeat the brake torque procedure and see if the noise persists, goes away, or changes frequency or tone. If the noise is still there - you probably have a heavily worn belt or a bearing is bad in one of the pullies (would include accessories, like the alternator pulley, A/C compressor pulley, P/S pulley, etc.)
2002 Corolla S, Silverstream, 1.8L 1ZZ-FE (VVT-i)
2003 Matrix XRS, Cosmic Blue, 1.8L 2ZZ-GE (VVTL-i) - RIP
2009 Matrix XRS, Blue Streak, 2.4L 2AZ-FE (VVT-i)
