The turbo's easy to check. Try turning the impeller - it should be smooth, not gritty, and there should be no play in the shaft.
The outlet hose from the turbocharger should have a slightly oily film on its inner surface. Wipe some of this with a clean cloth - do any metallic particles come away? If so, the impeller is rubbing the housing, the bearings are in need of replacement - you could put a bearing+seal kit through it and it will be ok, but if it has been rubbing, some of the fan tolerances may be out - you'd be better replacing the turbocharger.
If there's no metallic flakes/powder in the pipe and the shaft is good, then a more common (quite common) cause for shrieking is a boost leak. Boost leaks are usually easy to spot - that aforementioned oil causes hard black spray deposits around them. Key places to look are the hose joins.
Another place to look is the EGR tube. On the intake side, the EGR tube undergoes boost pressures while being fed exhaust pressures from the other end (which is right near the turbocharger). Sooty deposits will reveal where there are cracks. Cracks in the EGR tube can cause that noise - blocking both ends of the tube is an acceptable solution (unless you work for EPA).
Finally, check the bolts holding the turbocharger to the exhaust manifold. The exhaust gasket can act like a reed in a woodwind instrument (mine did). Look for sooty emissions from around the flange.