I am getting a loud squealing noise when turning the wheel. Noise goes ahead after car has been running for a while. NO problem with steering. What could it be?

tighten up you alternater bolt the on the underside of the alternater but not to much or it will be too tight and wont steer for crap

It could be your accessory belt. It's got too much slack it in. Check the belt to see how "loose" it is. If it seems loose tighten up the alternator as indicated by "Anonymous."

On the Corolla Ae101/102 series 1994 to 1999 4a- FE engine it took me two marginally effective belt adjustments to realise that my problem was a separated harmonic balancer which was squeaking only when cold. These double thickness crankshaft pulleys are so thick that they can go on slipping for many months when cold but work OK when hot - but the noise on cold starting cannot be permanently fixed by belt adjustment . Eventually they fail altogether. To test a suspected balancer have a look at it closely - or spray water on it when cold. If badly worn the squeak will disappear and all belts if under full load may stop rotating while engine is running due to slippage - as happened to me. Solution is a new or second hand Harmonic Balancer. Cheers, Eugene.