sure it's not the belt that is causing the noise?

The terms can mess up a diagnosis here.

The compressor has a pulley w/bearing that is engine driven.  That
pulley and bearing spin any time the engine is running.

The clutch is the flat disc like object on the front of the compressor
and is connected via a shaft to the "guts" of the compressor.  When
the a/c is on that clutch is moved in to the pulley and spins the
internals of the compressor.

So when you say it works normally for a minute it makes a big
difference to know whether it works for about a minute and then starts
squalling regardless or it works for about a minute when you turn the
a/c on then starts to make noise.

If it does it all the time regardless of the system being off or on
then the bearing in the pulley is most likely going bad.  These can be
changed without changing the compressor if you can get to it.  In
practice it doesn't seem like anybody ever does that anymore....  they
just replace the compressor.

If it only does it when the system is running then you have a few
other possibilities:
The clutch could be worn or misadjusted
The compressor could have internal issues
The low pressure side could be blocked
The system could be overcharged (have you been adding refrigerant?)
There could be to much oil in the system (have you been adding
refrigerant with oil?)

A lot of shops will look at the system for free and let you know
what's wrong with it.  I would get a pro to diagnose it for you then
decide whether to take on the repair yourself or have someone else do
it.

          Steve B.