A squeal is from the belt 95% of the time. Pumps don't typically squeal...they groan, chatter, moan, etc...but they don't usually squeal. Belts squeal. At full lock, pressure builds high causing resistance within the pump, which transfers to the pulley. If belt is not biting hard enough against the pulley it slips, and that's where you get the squeal.
Replace or adjust belt. After multiple squeals, it's glazed...likely needs replacement and can't be adjusted properly anymore. Unless the pump is getting SO stiff and bound up from age or whatever that even a properly adjusted good belt slips under pressure and causes the squeal. Then in that case, the underlyling cause is indeed the pump.
Crank the wheels all the way to the right and then all the way to the left five or six times. That should bleed the system. Recheck the fluid level, If you still get squeal at the end of travel, then what Gus said.